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Analyzing the Taxonomy of Internet Business Models Using Graphs by Chiou-Pirng Wang and KwaiChow Chan

Analyzing the Taxonomy of Internet Business Models Using Graphs by Chiou-Pirng Wang and KwaiChow Chan
Not only did the World Wide Web expedite the arrival of the information age in the last decade, it had also inspired a business revolution. Internet business, despite its infancy, has bred an unprecedented number of creative Internet business models (IBMs). Given that there are many creative models, there still lacks a universal well-defined IBM taxonomy. It is a tremendous challenge to create a universal taxonomy for these business models. Not only one has to face the babble of different existing models, one also has to address the evolving nature of Internet business. Hence, the imminent question is simply: Is it possible to construct a universal business model that could explain the existence of all of the current models and prescribe the evolving nature of Internet business models? In this paper, we propose that a simple scheme based on Euler's graph, a discrete mathematical tool that can be used effectively to study existing Internet business models and their classification schemes. It is also used to accommodate evolving IBMs. Such a systematic and analytical scheme based on graph theory might then assist in the discovery of a unified taxonomy for Internet business models.


A survey of Internet business models
Graphic representation of Internet business models
Analyzing BERT taxonomies using graphic models





We have witnessed all kinds of business models sprouting up from the Internet. Yet we still lack a definitive way to classify these models. Before one can understand Internet business as a whole, one needs to understand Internet business models, especially those that are successful, and their classifications. Various investigators have suggested different schemes to classify Internet business models. As a consequence, a number of competing taxonomies exist today, but they are constructed from different perspectives. This creates confusion for both scholars and practitioners alike.

Another obstacle in classifying Internet business models (IBMs) is that many are still evolving, changing rapidly and dynamically. Evolving IBMs may render the taxonomy of today obsolete tomorrow. For example, used to sell just books, but now it sells an array of merchandise, which was inconceivable in a traditional business model. The problem was best summarized by Lee Price, Chief Economist for the Economics and Statistics Administration: "It's not just a question of taxonomy. It's one of evolving taxonomy." (Tedeschi, 2000; Tehan, 2000) Hence, some of the questions are: Among various taxonomies, which taxonomy should one use? Is there a standardized method for analyzing and gauging the validity of the various and/or evolving taxonomies?

In this paper, we propose that a simple scheme based on graph theory, a discrete mathematical tool, that can be used effectively to analyze existing Internet business models and their classification schemes. It also can be used to accommodate evolving IBMs. This analytical scheme might be able to assist in the discovery of a unified taxonomy for Internet business models. Ideally, a unified taxonomy would classify most, if not all, of the existing IBMs; accommodate evolving models; and, predict emerging IBMs. A unified taxonomy is essential for understanding the evolution of e-commerce and its role in the global economy.

A survey of literature about current Internet business models is presented in the next section of this paper. Graph notations and three basic types of IBM graph models are introduced in the section on the graphic representation of Internet business models. The relevance of graph models in analyzing current business models is presented in the section on BERT taxonomies.



A survey of Internet business models

A survey of the literature at the time of writing reveals that several IBM taxonomies exist. We focus on those advocated by Bambury (1998), Eisenmann (2002), Rappa (2000), and Timmers (1998). We collectively call the models of Bambury (1998), Eisenmann (2002), Rappa (2000), and Timmers (1998) the BERT models of taxonomy. Chronologically, Paul Timmers was the first (in 1998) to propose a taxonomy that classifies 11 categories of IBMs. That same year Paul Bambury, a musician turned businessman, concluded that there are two branches of IBMs, one that is native to the Internet (six models) and one that is transplanted (eight models) from traditional business. Michael Rappa (in 2000) proposed nine categories based on the Internet business models then observed. Recently (in 2002) Thomas Eisenmann concluded that there are eight categories of IBMs in his book Internet Business Models: Text and Cases. Table 1 summarizes the four BERT taxonomies.


Table 1: BERT taxonomies of Internet business models (IBMs).

Author of taxonomy
Number of models in taxonomy
Classification schemes of Internet business models
Paul Bambury

Transplanted Real-World Business Models (8):
Mail-Order, Advertising Based, Subscription, Free Trial, the Direct Marketing Model, the Real Estate Model, Incentive Scheme, and Business to Business

Native Internet Business Models (6):
Freeware Model, Library Model, Information Barter, Access Provision, Web Site Hosting & Other Internet Services, and Digital Products & The Digital Delivery Model

Thomas Eisenmann
Online Retailers, Online Portals, Internet Access Providers, Online Content Providers, Application Service Providers, Online Brokers, Online Market Makers, and Networked Utility Providers
Michael Rappa
Merchant, Advertising, Subscription, Brokerage, Utility, Community, Manufacturer, Affiliate, and Infomediary
Paul Timmers
e-shop, e-auction, e-mall, Third Party Marketplace, e-procurement, Virtual Communities, Value Chain Integrators, Collaboration Platforms, Value Chain Service Provider, Information Brokerage, and Trust Services


These taxonomies share some common features of IBMs, but their differences are very noticeable. The similarities can be found in, for example, Rappa's Merchant Model, Eisenmann's Online Retailers Model, Bambury's Mail-Order Model and Timmers' e-Shop Model. In fact, one would expect these taxonomies to be similar in nature but different in semantics. But an attempt to match models among the taxonomies reveals that these differences are more than semantics. Based on the meanings suggested by the titles of the BERT models and some common sense about the Internet, Figure 1 illustrates some plausible matches, marked by links, between Timmers' and Rappa's taxonomies and between Rappa's and Eisenmann's models. Only half of the models between any two taxonomies could be loosely matched. Even a superficial look at nomenclatures will show that many of these models are irreconcilable, as shown in Figure 1 below: Readers are strongly encouraged to find plausible matches and mismatches of models suggested by Figure 1. The same is true when comparing Bambury's 14 models to Eisenmann's, Rappa's, or Timmers' models respectively.

Figure 1: Comparison of Internet taxonomies
Plausible matches of models between Timmers and Rappa, and between Rappa and Eisenmann are marked by links.

Since all four taxonomies are describing the same phenomenon, business on the Internet, one may argue that the mismatch is due to semantics and that one should delve into the details of the models to find better matches. We did exactly that, but the mismatches did not seem to go away. The differences are therefore not from semantics but from the different viewpoints and methodologies each author used in classifying their models. Timmers justified his classifications of IBMs based on value chain construction/deconstruction and the degree of innovation of e-businesses; on the other hand, Bambury's classification scheme is strongly influenced by his philosophical view of the Internet's free flow of information. Eisenmann's and Rappa's taxonomies were based on extensive case studies, keen observation, and intuitions. Except for Timmers, Bambury, Eisenmann, and Rappa did not explicitly explain the rules and criteria they used to classify Internet businesses into their taxonomic models.

The differences found in BERT models are partly due to the differences in authors' viewpoints, but also because the nature of Internet business is not well understood. Internet business is still in its infancy, growing and evolving rapidly. The Internet is not only like a big elephant, it is also an evolving beast. It is quite likely that each of the BERT taxonomic models captures some unique aspects of Internet business not found in the other models. It is also quite possible that some business models have not yet been classified by the BERT models and that some emerging models might escape this classification.

Because of the filtered lens of the four authors and the evolving nature of the Internet, the current BERT system lacks a clear-cut way to define IBMs unambiguously. A reader not familiar with the terminology may be baffled by how the same Internet business can be classified one way by one taxonomy but in a very different way by another taxonomy. For example, is categorized as an Infomediary Model by Rappa but as an Internet Access Providers Model by Eisenmann. If Infomediary and Internet Access Providers are two different models, then how can both be correct? If they are not both correct, which one is? If these two models were not entirely independent, could they be both correct, both wrong, partially correct or partially wrong? If they are both correct, could these two models be merged into a single new model? Or could they both be valid because they address different concerns through different filtered lenses? If so, could each of the classifications of BERT be valid in its own right? Or maybe diversity in modeling simply means that there is lack of a common consensus about what to classify and how to classify? Could there be an alternative way to classify Internet businesses and iron out the differences and consolidate the similarities of BERT models or models yet to emerge? These are some of the questions this paper attempts to address and we believe that we have a few answers.

In order to understand the phenomenon of Internet business, it is important to be able to classify all types of thriving business models currently in operation and their evolutionary trends. However, the proliferation of taxonomies such as the BERT models only hinders progress in understanding Internet business, instead of promoting it. Practically, one universal or dominant model would be preferred. A universal business model taxonomy should do what the Linnaean system did for our understanding of life on Earth. Ideally, a universal model should obey these criteria: (1) the model is comprised of a general theoretical framework that all observable models could be derived from; (2) the model is capable of explaining the differences and similarities classified by BERT and other emerging taxonomies; and, (3) the model is capable of classifying new and evolving models.

It is our hopes that our graph approach will satisfy the criteria above. A graphic approach to IBMs will first be applied to analyze BERT models and demonstrate their potential. But before venturing into graph models, some basic graph terminology will be introduced in the next section.



Graphic representation of Internet business models

Graph theory was introduced by luminary Swiss mathematician Euler in 1736. Graph theory has long been recognized as one of the most useful mathematical subjects for modeling electrical circuitry, molecular diagrams, mathematical relations, transportation problems, pipeline networks, economics, psychology, computer science, and even biology (Ore, 1963). In mathematics, graph theory is classified as a branch of topology but is strongly related to algebra and matrix theory. In this article, graph theory is used as a tool to analyze IBMs qualitatively. Quantitative models are under consideration.

Graph related definitions

A graph, denoted as G(V, E), is a structure or diagram that consists of a set of nodes called vertices represented by a set, V={ v1, v2, ...}, and a set of line segments joining the nodes together, called the edges E = {e1, e2, ...}. The degree of a vertex v, d(v), is the number of edges incident with the vertex v (Gross and Yellen, 1999; Ore, 1963; Even, 1979; Leibniz, 2002). A collection of graph examples from an isolated graph to a graph of five nodes by 10 edges is shown on Figure 2. Graph 2-A is an isolated graph with one vertex and zero edge. Vertex v is isolated and has 0 degree; Graph 2-B is a graph of two vertexes, v1 and v2, and one edge. v1 and v2 are the end point of edge e1 and has one degree; Graph 2-C illustrates a graph of three vertices and two edges. A closed examination of graph 2-C reveals that the Graph 2-C has three vertices expressed as V = {v1, v2, v3} and two edges expressed, as in the Figure 2-C, E = {e1, e2}. V1 and v3 of Graph 2-C are endpoints of the edge e1 and e2 respectively, so each of these vertices has only one degree: d(v1) =1 and d(v3) = 1. Vertex v2 is the endpoint of both edges e1 and e2; therefore v2 has degree 2, or d(v2) = 2. On the other hand, Graph 2-D has five vertices and 10 edges (V= {v1, v2 ... v5}, E= {e1, e2 ... e10}) and each vertex has degree 4. Graph 2-D demonstrates a graph with five vertices and 10 edges. Every vertex in Graph 2-D is degree 4. Hence number of vertices and edges of a graph varies from graph to graph. The degree of a vertex in a graph varies from vertex to vertex.

Figure 2: Graph examples
A graph is a structure composed of vertices and edges. Graphs A - D illustrates four examples of graphs. Graph A is an isolated graph. Graph B has two vertices that are connected by one edge. Graph C has three vertices and two edges. Graph D has five vertices and 10 edges. The number of vertices and edges of a graph thus varies from graph to graph. Degree is defined as number of edges terminated at a vertex. Vertex v2 of Graph B has a degree of one, v2 of graph C has degree of two, and v2 of graph D has a degree of four.

A graph that has an arrowhead added on the edge e1 as shown in Figure 3 is a directed graph, or a digraph. A digraph is similar to a graph except that the pair of endpoints of an edge is now ordered; the first endpoint is called the start-vertex of the edge and the second endpoint is called its end-vertex. The edge, e1, is then said to be directed from v1 to v2. The outdegree, dout(v), of a vertex v is the number of edges which have v as their starting vertex; likewise indegree, din(v), is the number of edges which have v as their ending vertex. Figure 3 is a digraph with ordered edge,e1, which starts at vertex v1 and end at vertex v2; the outdegree of v1 is equal to the indegree of v2, so dout(v1) = din(v2) = 1. In the next section, vertices and edges are used to represent business actors and transactions respectively.

Figure 3: Digraph
A digraph is graph whose edge is ordered such that the ordered edge, e1, starts at vertex v1 and ends at vertex v2.

Graph representation of an Internet business model

The graphs introduced in the previous section can be used to represent Internet business models. Three basics types of graph models can be useful for representing Internet businesses: namely a Gift Model, a Direct Exchange Model, and an Indirect Model. These three graph models will be used as building blocks to analyze or construct Hybrid Models that are composed of two or more of these three basic types. Before graph models are introduced, there is a need to clarify the definition of an Internet business model.

Definition of an Internet business model (IBM)

The term "business model" is not well defined despite the fact that it is so pervasively used. This term has been analyzed by some, including Osterwalder and Pigneur (2002), Chesbrought and Rosenbloom (2000), and Afuah and Tucci (2000). According to Rappa (2000), a business model is a method of doing business by which a company can sustain itself. Paul Timmers (1998) on the other hand suggests that the definition of a business model should include the following:

Based on these two versions of definitions, we define an IBM as a business model that satisfies descriptions suggested by both Timmers and Rappa and add that the business must use the Internet as its primary means to generate values or revenue over the long term. In this paper we postulate a graph approach to differentiate various forms of IBMs based on the way money, information, products, or services flow among various business actors. Each transactional flow is interpreted as a business interaction between two business actors. An IBM is thus classified by the types of transactional flows among actors — not by detailed business processes, the nature of products or services, the value chain of the business, nor the types of customers the business is serving, although these details may prove useful in differentiating closely related business models. This approach will free us from details and allow us to stay focused on classifying IBMs in broad categories based on the structure of interactions among business actors.

With this approach in mind, it is now possible to represent an IBM based on the graph terminology introduced in the last section. First a vertex is used to represent a business actor. The business actor can be a seller, a customer, a broker, or some other actor; an edge is used to represent a transaction between two actors; an arrow on an edge represents the direction of the transaction; and, the degree of a vertex indicates the complexity of interactions that a vertex (a business actor) has with other vertexes. Figure 4 represents a simple IBM, illustrating a seller exchanging service, information or product (indicated as SIP) for SIP or for money (indicated as $) from a buyer online. The vertex, v2 represents the seller who sells or provides SIP to v1 the buyer, who consumes the SIP and pays an equally valued SIP or money, $, in return to the seller (v2). From the point of view of transactional flows (interactions among actors), a graph such as Figure 4 is adequate to represent what an online storefront business is doing: selling products or services or information in exchange for money from customers.

Figure 4: Graph representation of an Internet business model
An Internet business model is represented by a graph in which online seller is represented by a vertex v2 selling a SIP in exchange for revenue or a SIP from the buyer who is represented by vertex v1.

Definitions of vertices and edges in an IBM graph model

Throughout this article, vertex symbol v1 will represent the buyer, consumer, or user while v2 will represent the seller, provider, or other business entity. In the role of business actor, the word "buyer", "consumer", and "user" will be used interchangeably and so will "sellers" and "providers". Vertex v3 typically represents a third party, a facilitator, or a mediator that facilitates the exchange between the v2 (seller) and v1 (buyer). If a business actor plays dual roles as a buyer and a seller at the same time in a business model, v12 is used. If there is a need to differentiate a class of actors, such as buyers, sellers, or facilitators, who are similar in nature, a prime symbol will be used such as v1_, v2_, v3_ or v12. in contrast to v1, v2, v3 or v12 respectively. An edge represents a transactional flow. The flow could be payment/revenue ($), or a service (S), information (I), or a physical product (P). Collectively, SIP is an acronym for service, information, and/or physical product. Whenever SIP is used to represent a transactional flow, the flow could be S, I, or P or a combination of them: SI, SP, IP, or SIP. So a SIP flow doesn't necessarily represent all three flows occurring simultaneously, though they could. Whenever there is a need to distinguish two transactions of similar type such as $-flow, then a subscript will be used, e.g., $1 and $2 (pronounced as "dollar 1" and "dollar 2").

Point of reference

One of the major sources of confusion in defining business models is that the point of reference is not clearly identified to readers in some of the BERT business models, and for that matter, of other business models. Some business models are product-centric and some are revenue-centric. Even in the same taxonomy, business models do not always have the same point of reference. In order to avoid the traps caused by moving reference points, all business models analyzed and/or defined in this paper will assume the central viewpoint of the Internet business of interest. For example, NetZero operates under Gift Model from the point of view of the users or consumers because they really get the service for free, except they have to bear with advertisement banners and exposing their Web habits. To observers, particularly scholars like us, who study Internet businesses but not the players in the model, we firmly believe that the model is not free. According to Observer A, NetZero is operating as an Advertising Based Model because it derives part of its income from advertisers; hence the central viewpoint is on the source of income or $ flow. However, Observer B may claim that the business model is in fact an Internet Access Providers Model (Eisenmann) because it provides free access to users but draws revenues from advertisers. So the Internet Access Providers Model is absolutely correct from Observer B's point of view but nonetheless a relativistic perspective. The problem with these points of view is that the business could be categorized by yet another observer as an Infomediary Model if the observer emphasizes that NetZero attracts information buyers in the business sector who are interested in information collected and processed by NetZero. Classifying business models based on these viewpoints creates confusion because the interests of individual observers vary and so do the terminologies they use. We believe the best policy is to use the business' point of view. Otherwise the authors of any IBM taxonomy should clearly state their points of references in constructing their models. Indeed from NetZero's point of view, it wants to maximize its profits by gaining as much revenue as possible. It attracts advertisers by drawing a large audience of users to its service. It then views the users who use its free Internet access service as a resource, securing its users profiles and selling them to other businesses. To NetZero, users, advertisers, and business information buyers are all its customers but advertisers and business information buyers are paying customers. To attract users, NetZero provides free Internet access services, but whether its users actually make purchases from advertisers is not a fundamental concern in NetZero's business model. In this viewpoint, the interaction between advertisers and NetZero's users is not considered a part of the Internet business model for NetZero. To advertisers, the influence of advertisements on the users is very important. Basically NetZero is a creature with two sources of income, one siphoning in raw materials (user information), and one service leg (an Internet access service). To survive, this business will not remain static but will continue to evolve until it can find other sources of revenue to sustain itself.

Hence, if all business models are described from the company's point of view, some confusion will be minimized. All analysis of IBMs within this paper is based on this point of view: Defining and analyzing IBMs in BERT models based on the company's point of view with the help of graph models. The company running the Internet business is considered as the primary actor in its business model.

Three basic building blocks of IBM graph models

Three graph models are proposed to serve as the basic building blocks for analyzing existing IBMs which may be evolving or for synthesizing new IBMs. These three basic models are the Gift Model (GM), Direct Exchange Model (DEM), and Indirect Model (IM). These three basic models can be combined to synthesize new or more complex IBMs. Any synthetic model is treated as a Hybrid Model.

Gift Model

According to Rishab Aiyer Ghosh (1998) most Web sites are created by amateurs who expect no financial return. Even today, much of the interaction on the Internet is not financial, but may involve the accumulation of value such as "reputation capital" that could be potentially transformed into business models. The Gift Model is thus introduced to capture this class of business. The Gift Model is represented by a digraph with two vertices and a directed edge; see Figure 5. The transaction of SIP (a directed edge marked with SIP) is one way from the seller vertex, v2, to the buyer vertex, v1. The seller vertex v2 (the source) has an outdegree of 1 and an indegree of 0; while the buyer vertex v1 has an indegree of 1 and no outdegree. At a glimpse, a Gift Model shouldn't be considered as a business model at all because it doesn't generate revenue. However, free flow of information is the fundamental nature of the Internet (Bambury, 1998). According to Bambury, such types of IBMs are categorized as native Internet business models.

There are different kinds of free models. Some are conditionally free, some are free for a limited time, some provide free features but offer advance features for fees, some are free because startups are trying to establish themselves. Whatever the reason, we categorize them under the Gift Model. Businesses that survive on the Internet successfully take advantage of the nature of the free flow of information to help generate values or revenues from different business actors in the long run. A typical successful Gift Model is As a portal provider, in its earlier stage provided information absolutely free. Later used advertisement banners, content, and services to generate revenue. Today, has evolved into a global brand with $776 million in transactions during the first quarter of 2002 (Yahoo! Media Relations, 2002). Yahoo still hasn't abandoned its role as a portal which still keeps the Gift Model as a component of its business model. However, no business can survive solely on a pure Gift Model for a long period of time. Typically a Gift Model gives away SIP or some SIP for free but generates revenue by other means or at a later time. For example CuteFTP gave away software that facilitated file transfers between computers over the Internet for free. Once CuteFTP dominated the FTP users' base, it switched to a fee-based model. However, it has not abandoned its Gift Model with a modified version of CuteFTP (with fewer functions) still available for free. AOL achieved phenomenal success by offering Internet access for free for a month to new users. AOL took advantage of a Gift Model and then evolved into a different model later as a viable strategy. When a user retrieves free but useful information from a Web site, the Web site is said to have a Gift Model as one component of its business model since it creates value to the business actor.

Figure 5: Gift Model
The Gift Model is represented by two vertices (actors) and a directed flow from one actor into the other. The flow could be service, information, or any tangible or intangible product (SIP). Since v2 delivers SIP without receiving payment from v1, it is a gift.

Direct Exchange Model

In the Direct Exchange Model, sellers exchange services, information, or products (SIP) for payment ($) or a SIP from the buyer. A Direct Exchange Model has already been represented graphically in Figure 4. This model consists of two vertices (actors) and two directed edges (transactions): SIP-$ or SIP-SIP. Each vertex, v1 or v2, has both an outdegree of 1 and an indegree of 1. This model, as seen in Figure 4, expresses the exchange between two actors (buyer vertex v1 and seller vertex v2) through directed SIP flow and $ flow. The interaction pattern between the primary actor and the buyer in a Direct Exchange Model is one-to-one since a sale involves only one buyer and there is no information aggregated and integrated from many buyers to make the sale. A typical example of the model is

Indirect Model

When a third party is involved to facilitate the exchange between the seller and the buyer, the business model is classified as an Indirect Model. The Indirect Model is really the business model of brokers or market makers, transactions that happen between a buyer and seller resulting from the service or infrastructure provided by a third party. The graphic representation of the Indirect Model consists of three vertices and at least three edges. Figure 6A to Figure 6D illustrate four possible types of the Indirect Model. Besides the normal buyer (v1) and seller (v2) pairs at the horizontal level, a third vertex, v3, is added to the graph, a level above the buyer and seller vertices. In the Indirect Model the primary actor in focus is the third party, v3 (acting as a facilitator) and the interaction flows between the primary actor and the other two actors, v1 and v2. The role of the third party (v3) is to, but not limited to, facilitate the business transactions between buyer and seller by providing value-added services or infrastructure. The middleman or facilitator, v3, generates revenue only when a successful fulfillment happenes between the seller and the buyer. The facilitator (v3) generates revenues from seller or buyer or both in four possible manners. The way the revenue is generated by v3 defines the type of Indirect Model. BERT classifications contain four different types of Indirect Models: Type I, Type II, Type III, and Type IV.

Figure 6A: Type I Indirect Model
The graph is consisted of three vertices and three edges. The third party v3 provides services to both the buyer v1 and the seller v2 but receives its revenue only from v2. The dot lines between v1 and v2 indicate a successful sale between the two as a result of the service of v3.

In the Type I Indirect Model, the third party (v3) charges the seller (v2) for setup fees, transaction fees, commission, and/or listing fees (see the transaction between v3 and v2 on the right side of Figure 6A) if the transaction between the v1 and v2 is fulfilled. Not merely catering to the need of the seller, the third party facilitator also provides SIP that are not provided by the seller to the buyer (see the left side transaction between v1 and v3 of Figure 6A) as a result of v3's service, any potential exchange between v1 and v2 represented by the dotted line. Examples of Type I IM are,,, and

In the Type II Indirect Model, the third party (v3) charges fees to the buyer. Figure 6B illustrates this model. Notice that the revenue flow is originated from the buyer (v1) to the third party v3. See the transaction between v1 and v3 on the left side of the Figure 6B. With the revenue derived from buyers, the third party can afford to provide service to the seller v2 as well. Again as the the consequence of v3's service, any potential exchange between v1 and v2 is represented by the dotted line. An example of Type II IM is to which a hospital pays fees for the placement of nurses.

Figure 6B: Type II Indirect Model
This model is similar to Type I except the third party v3 derives its profit only from the buyer while providing services to both the buyer v1 and the seller v2. The dotted lines represented the direct exchange of v1 and v2 as a result of the service provided by v3.

In the Type III Indirect Model, a middleman (v3) generates revenue from the difference between buyer's payment and seller's sale price as illustrated on Figure 6C, where the buyer (v1) pays payment ($1) to the third party (v3), which in turn pays the seller (v2) the sale price ($$2$), which is less than the payment. The difference ($$1$-$$2$) becomes the revenue of the middleman. One example of Type III IM is the service of selling plane tickets provided by

Figure 6C: Type III Indirect Model
The third party v3 provides services to both seller v1 and buyer v2 and generates revenue by keeping the difference between v1's payment and the seller's sale price.

The three graphs Figure 6-A, 6-B, and 6-C are composed of three vertices and three to four directed edges. The common characteristic of all three types of Indirect Model is that the third party (v3) either serves as facilitator or middleman and has to provide services or infrastructure to both the seller (v2) and the buyer (v1) in order to make business transactions between v1 and v2 happen. In other words, v3 (third party) has at least two SIP arms and one or two revenue arms. In the graph language, v3 has outdegree of two, dout(v3) = 2, forming two SIP edges. Of course there should be at least 1 indegree of revenue, either from the seller or buyer, hence din (v3) = 1, minimum.

In fact, several existing IBMs of BERT such as Online Brokers, Online Market Makers, e-auction, etc., to be discussed later, belong to these three types of the Indirect Models. There is no reason the revenue can't come from both the buyer (v1) and seller (v2). When this happens, we simply inverse the direction of $2 edge in Figure 6C to form yet another Indirect Model as shown in Figure 6D. This is the Type IV Indirect Model. An example of Type IV IM is Both buyers and sellers who exchange stocks need pay eTrade the transaction fee based on the amount of transaction. This is the beauty of graphs, because they allow one to systematically assign different types of business models based on the revenue ($) and SIP exchange between actors.

Figure 6D: Type IV Indirect Model
The third party v3 provides services to both seller v1 and buyer v2 and generates revenue from both of v1 and v2.

Hybrid or Compound Models

There are IBMs in BERT taxonomies that are not described by the Gift Model, Direct Exchange Model, or Indirect Model alone. However, they could be synthesized by using these three basic building blocks. Figure 7A is an example of a Hybrid Model composed of two of the basic building blocks, a Gift Model and a Direct Exchange Model. The portal and advertisement service of is an example of this model. Figure 7B shows an example of a hybrid composed of two Direct Exchange Models, a two-tier system. One scenario suggested by the Hybrid Model of Figure 7B is that the primary business actor v12 whose business model is to barter with v2 and then sells SIP to v1. Effectively, this is Rappa's Infomediary Model. is an example of this model. Other obvious possibilities for Hybrid Models would mix Direct Exchange Model with Indirect Model, or would combine all three basic building blocks.

Figure 7A: A Hybrid Model Example 1
This Hybrid Model is composed of a Gift Model and a Direct Exchange Model. An example of such Hybrid Model is Eisenman's Online Portals Model.

Figure 7B: A Hybrid Model Example 2
This Hybrid Model composed of two Direct Exchange Models. An example of such a Hybrid Model is Rappa's Infomediary Model.



Analyzing BERT taxonomies using graph models

The three basic types of graph IBMs defined in the last section can now be applied to analyze IBMs classified by the BERT taxonomies. This analysis provides insights into IBMs and resolves some differences found in the BERT classifications. It is important to point out that these basic graph models are constructed to facilitate the analysis of IBMs outlined by the BERT taxonomies as well as emerging models. To avoid confusion that can result from different reference points mentioned earlier, all IBMs will be analyzed based from a company's point of view and represented by graphs. The graphs are not meant to serve as an independent IBM taxonomy though it is possible to construct a graph-based taxonomy. For instance, the Direct Exchange Model encompasses many existing business models, such as a merchant model, mom-and-pop model, subscription model and so on. In fact, any model that involves two actors exchanging SIP with money or another SIP is classified as a Direct Exchange Model regardless of the nature of the services, information and/or products exchanged. The Direct Exchange Model is therefore not a new model but a generalization of many existing BERT models. The same is true of the Indirect Model and hybrid models. Though not a taxonomy, these basic graph models could help define, analyze, and strengthen a taxonomic analysis.

If the degree of generalization in a graph does not tell the difference between, an Online Content Providers Model (Eisenmann), and, a Merchant Model (Rappa), what use are graph models? Selling digital content is indeed very different from selling books. Practically, there is no inventory associated with digital content, no boxes to be shipped; users also pay year-around subscriptions. Although the business processes and the types of products of these two business models are very different, their essence is the same. Each is a two-actor system in which seller and buyer exchange money for SIP. With this level of abstraction, one can quickly spot service/information/product types and role(s) of the business actor. Any deviation must be a distinctly different business model. Another reason to use this level of abstraction in graph is that virtual world (Internet) businesses can much more easily change their modes of operation than real-world (physical brick-and-mortar) businesses. It is difficult enough for a brick-and-mortar bookstore to expand into a WalMart-like store, which is selling electronics and cookware among things and serrvices. But technology makes it quite possible in the world of Internet businesses. So when expands its lines of products from books to DVDs, electronics, home improvement tools, and software to plane tickets (through, auction services, or to e-books or online content, its basic business model is changing dynamically. If, on the other hand, any deviation from this model does occur, it could be easily detected with the help of the graphic approach. Indeed,'s model is more complex than a Merchant Model (Rappa) or Online Retailers Model (Eisenman), a point to be discussed later.

A highly generalized graphic model thus simplifies the task of analyzing an Internet business that is dynamic in nature without losing track of its rapid evolution. Any concern that the tradeoff is over simplifying the traditionally well-defined models can be easily overcome by supplying specifics to the general model. In another words, if x is a variable representing an object, then whenever there is a need to specify x, all one has to do is to name an object with leaves and a trunk as "tree". When there is a need to specify the difference in products of the Direct Exchange Model then one can simply branch them out by labeling them and characterizing them as Content Provider or Retailer, for example. Two models are now derived from a general Direct Exchange Model.

Applying the Gift Model to analyze BERT taxonomy

Though a simple Gift Model doesn't sound like a business model, there are some examples such as yahoo and Netscape that started using the Gift Model in the beginning phase of their operation. Eventually they evolved into a Hybrid Model but they keep their original Gift Model as a critical strategy to attract new customers. A graph representation of a simple Gift Model has already been shown in Figure 5. and were good examples of Gift Model when they were startups. Neither company operates as a pure Gift Model now but when they first launched their Web sites, their services or software were free. So the Gift Model Graph serves as standalone model that represents all those Internet businesses that operate in a free mode for some period of time. Though many established dotcoms have evolved into for-profit models, they retain their original free strategies. The Gift Model exists now as part of a Hybrid Model, not as a standalone model. For instance, provides free downloads of its Acrobat Reader, offers one month to 45 days of free Internet access to some classes of users, and CuteFTP has certain trial period for its software. A common component among these companies' graphic representations is shown in Figure 7A.

Using the proper frame of reference, it is found that the Gift Model only applies to the Library Model in Bambury's taxonomy. Other so-called free models in Bambury are conditionally free; they are in fact mixed models. The Gift Model is useful as part of a hybrid model which has a free component.

Applying the Direct Exchange Model to analyze BERT taxonomy

A simple Direct Exchange Model consists of two vertices and two directed edges as shown in Figure 4, with vertex v2 and v1 representing the seller and the buyer respectively. The two transactions could be either payment-to-product exchange ($-SIP) or product-to-product exchange (SIP-SIP). See Figure 8-A and Figure 8-B. Plenty of online businesses can be represented by a Direct Exchange Model graph. For instance, sells shoes online; sells online content; and, at UK provides legal consultant service online. Regardless of the service or product types, all two-party exchange is branded a Direct Exchange Model graph. Several BERT IBMs possess the properties of a Direct Exchange Model graph. For instance, Bambury's Mail-Order and Information Barter Models, Eisenmann's Online Retailers, Rappa's Subscription and Merchant Models, and Timmers' e-shop Model all have Direct Exchange Model as the primary feature (see Table 2).

Figure 8: Direct Exchange Model
Graph A is a payment-to-product ($-SIP) Direct Exchange Model, while Graph B is a product-to-product Direct Exchange Model (SIP-SIP).

Examples of SIP-SIP Direct Exchange Model (barter model) are,, and (Sol, 2002) is an open source code applications provider providing software developers with host services such as training and free software tools. Members of this network handle questions from a variety of individuals. Developers with reputations gain business by referrals and answering queries. So barter is treated as a core business model in the case of


Table 2: Existing IBMs categories analyzable by graphs.

Gift Model
Bambury: Library Model
Direct Exchange Model

Bambury: Free Trial, Direct Marketing, Digital Products & Digital Delivery Model, Mail-Order, Subscription, Real Estate, and Information Barter Model
Eisenmann: Online Content Providers (e.g., Online Retailers
Rappa: Merchant, Subscription (,, Utility, (e.g. Authentical), and Community Models (e.g., Guru, Exp)
Timmers: e-shop, Virtual Communities, and Value Chain Service Provider

Indirect Model

Eisenmann: Online Brokers and Online Market Makers
Rappa: Affiliate Model and Brokerage Model
Timmers: e-auction and e-mall

Hybrid Model
Bambury: Freeware Model, Web Site Hosting & other Internet Services, Advertising Based, Incentive Scheme, Business To Business, and Access Provision
Eisenmann: Internet Access Provider, Networked Utility Providers, Online Portals, Online Content Providers (e.g.,,, and Application Service Providers (e.g. USi, Corio)
Rappa: Subscription (e.g., Manufacturer Model, Infomediary Model, Community Models (e.g. ExpertCenter, Deja, Abuzz), and Advertising
Timmers: Virtual Communities, Information Brokerage, Collaboration Platforms, Third Party Marketplace Providers, E-Procurement, Value Chain Integrators, and Trust Service


It is interesting to point out that Rappa's Community Model (or Timmers' Virtual Communities Model) is a special kind of Direct Exchange Model. The graph representation of this IBM is better depicted by Figure 9 than by Figure 4, where a solid line is replaced by a dotted line. A dotted line is used because in the Community Model, payment (or contents) only occurs when the user or consumer chooses to pay (or provide for the service). Therefore dotted lines are used to represent an optional or a potential flow. Before the payment occurs it is a Gift Model. When the users elect to pay, the model switches into Direct Exchange. The oscillation property of a Community Model is actually an irregular Direct Exchange Model. Bambury's Free Trial and Direct Marketing Models have the same characteristics as Rappa's Community Model. It is only with caution that this analysis is valid when applied to examples cited in Rappa's Community Model. The Community Model in general may be more complicated than Rappa's model. IBMs listed in Table 1 were analyzed one at a time, example by example, systematically by using graph theory; those found describable by Direct Exchange Model are listed in Table 2.

Figure 9: Graph Representation of Rappa's Community Model
In this model, the payment flow may or may not materialize. If not, the model falls back into a Gift Model where the user gets SIP for free; when the user decides to contribute, the model switches into a Direct Exchange Model. A dotted line is used to express that there is potential for the payment to occur. This model is based on Rappa's Community Model.

Applying the Indirect Model to analyze BERT taxonomy

All Indirect Models contain three vertices with at least one incoming revenue edge and two outgoing SIP edges, one toward the seller (v2) and the other toward the buyer (v1), as shown in Figure 6A, 6B, 6C and 6D. Rappa's Brokerage, Timmers' e-mall and e-auction, and Eisenmann's Online Brokers and Online Market Makers are all examples of Indirect Model.

An analysis of all IBMs in the BERT taxonomies indicates that there are four types of the Indirect Model, depending on how the revenue is generated. As mentioned earlier if the third party (v3) acts as a facilitator who gains revenue from the seller, it belongs to Type I Indirect Model, e.g., and; If the third party, (v3), gains revenue from buyers then it is Type II Indirect Model, e.g., is a typical example of Type III Indirect Model because as a facilitator it derives its profits from the difference between the buyer's paid price and the seller's bid price. On the other hand, eTrade is an example of Type IV Indirect Model because it charges both seller and buyer.

It is interesting to note that the Indirect Model can be applied effectively to analyze the e-auction Model exemplified by and also to infer the existence of the reversed auction model pioneered by When a graph is used to represent the e-auction Model, it intrinsically contains three edges and three vertices — the buyer (v1), the seller (v2), and the facilitator (v3); see Figure 10. However, the status of buyer is limited to the owner of the winning bid. The potential buyers (bidders) are represented by a column of vertices, a set G, shown in Figure 10. Out of this list of bidder vertices, only the winner, who is denoted by the darkened vertex, emerges as the buyer. First, eBay has to provide online bidding services to a group of bidders who bid on products they are interested in, then eBay gathers the bidding information from the bidders to sort out the winner of a product, and finally eBay links up the winner and the seller. This service is free to the bidders but not the seller. Since the bidding information from a group of bidders has to be aggregated and integrated, the interaction pattern between the seller and the buyer(s) is one-to-many. Therefore a set G of vertices (buyers) instead of a single vertex used to represent this one-to-many interaction pattern. Since caters services to both the buyer and the seller but derives its revenue only from the seller, eBay operates in Type I Indirect Model. This conclusion could be made clear by comparing Figure 10 to Figure 6A. The dotted lines between v1 and v2 indicate a successful sale between the two as a result of the service of v3.

Figure 10: Graph Representation of the e-auction Model
An e-auction is a Type I Indirect Model with one-to-many interaction pattern.

The reversed auction model pioneered by is just as easy to capture using graphic representation; see Figure 11 as the e-auction model. In the reversed auction model it is the seller who has to bid for the business from the buyer. So a group of potential sellers, G, have to submit bids for the business and only the winner (v2), represented by the darken vertex, could become the actual seller. In the reversed auction model acts as the mediator (v3) who administrates the bidding, collects payment from the buyer, pays the seller and keeps part of the payment as profits when a successful sale is secured. The reversed auction model is depicted in Figure 11 where the mediator,, derives its payment, $1, from the buyer (v1), and in turn pays the seller (v2), the sale price, $2, which is less than the payment. The difference ($1-$2) becomes the revenue of This renders a Type III Indirect Model. A comparison graph of the e-auction model, Figure 10, and the graph of reversed auction model, Figure 11, reveals that the major difference between the two is the way revenue is derived on one hand and the actors (vertices) are placed on the other hand. To convert Figure 10 into Figure 11 all it takes is to add an extra $-flow to facilitator (v3) and switch the buyer (v1) with the seller (v2). The interesting fact is that the reversed auction could have been discovered by manipulating elements (three vertices and edges) of a graph alone. In other words, by enumerating the graph elements systematically, one could have come up with the reversed auction model without the intuitive insight of On the surface most people would think was a stroke of genius. But the graph analysis indicates that it's quite feasible to derive it systematically. The fact that a graph could easily infer a new model from an old one indicates it is a good tool for building and analyzing IBMs. All IBMs in the BERT system that can be analyzed by Indirect Model are tabulated in Table 2.

Figure 11: Graph Representation of a Reversed Auction Model
A reversed auction is described as a Type III Indirect Model.

Applying Hybrid Models to analyze BERT taxonomy

All IBM models that can't be classified directly as a simple Gift Model (GM), Direct Exchange Model (DEM) or Indirect Model (IM) are considered hybrid models. It is postulated that a hybrid model is a combination of these three basic building blocks: GM, DEM, and IM. The proof is analytical and is still under development. Hence there are no standard graph representations of hybrid models per se. A hybrid comes in various forms. Not all hybrid models started up as hybrid; many were found to evolve from the simple (GM, DEM, or IM) blocks into a more sophisticated Hybrid Model. An Internet-based business often uses multiple models of IBM to conduct its business. Rappa's Manufacturer Model can be described by a Hybrid Model as illustrated in Figure 12. The Manufacturer Model is actually a synthesis of two Direct Exchange Models. In this hybrid model, there are three vertices and four directed edges. The manufacturer (v2) may sell products to the buyer (v1) through a distributor (v12), who plays the role of buyer relative to the manufacturer (the primary actor) but the role of seller relative to v1. From the end buyer's point of view, v1 can purchase products from the manufacturer through two paths: Buy indirectly from the distributor v12 or directly from the manufacturer by v2. From the manufacturer's point of view, it is selling products to two types of buyers, end consumers and distributors. Since the distributor might sell to the same end buyers (end customers), the Manufacturer Model raises a red flag on this issue of channel conflict. Together this Model, captured by Figure 12, is in fact a two-armed Direct Exchange Model, this is, a Hybrid Model. This is not a simple Direct Exchange Model because the customers are two very different types. The traditional Manufacture Model doesn't sell direct to consumers, so from the manufacturer's point of view, a traditional Manufacturer Model is a simple Direct Exchange Model. The Manufacturer Model as an IBM was first coined by Rappa. Notice that in this so-called Manufacturer's model, there are two sources of revenue going into v2 and two SIP flowing out of v2. So the number of indegree is thus equal to that of the outdegree, both are two. Ideally the more channels of revenues, the better it is for business if channels are not in conflict. There is no reason why one can't generate a model that includes more channels of revenue. In fact some manufacturers are selling surplus or overstock through eBay to open other channels of revenue without inflicting channel conflict. Obviously, graphs can help conceptualize these new models and spot potential conflicts. If we want to use a graph to represent the wholesaler's business model, we can simply shift the centric viewpoint to the wholesaler (v12), drop the two edges between v1 and v2 in Figure 12, then turn the dotted lines between v1 and v12 into solid lines. This change turns Figure 12 into Figure 13.

Figure 12: Manufacturer Model — A Hybrid Model
This hybrid IBM model is a combination of two simple Direct Exchange Models. v2 is the manufacturer, v12 is the distributor, and v1 is the end customer.

Figure 13: A Graph Representation of a Wholesaler's Business Model in the Supply Chain
This Hybrid Model contains two simple Direct Exchange Models. v12 is the wholesaler, v2 is the manufacturer, and v1 is the end customer.

The application of graph theory proved to be useful when it was used to resolve a confusion caused by Rappa's Infomediary Model and Eisenmann's Internet Access Providers Model. Both models cited as an example. Apparently not all online access business is Infomediary nor vice versa. After the analysis, it was found that both Rappa and Eisenmann emphasize different aspects of the Netzero business model to support their modes of categorization. Figure 7A and Figure 7B illustrate the graph representation of Rappa's Infomediary Model and Eisenmann's Internet Access Providers Model for respectively. The Netzero as Rappa's Infomediary is a hybrid model with two tiers of DEM model. The Netzero as Eisenman's Internet Access Providers Model is a combination of one Gift Model and a Direct Exchange Model.

The graph showed in Figure 7B captures the essence of Rappa's Infomediary Model. In this graph model, the information dealer marked as v12 in Figure 7B acts as a buyer who collects data from online browsers or consumers (in fact is seller marked as v2) by offering them free Internet access service. The information dealer then processes and analyzes data collected from v2 (the user), changes its role from buyer to become a seller and sells the processed information to information buyers (v1) who are merchants, marketers, or even consumers themselves. Certainly from a revenue point of view, operates in this Infomediary Model. But to service (or user) point of view, NetZero provides online access. Eisenmann classified in the Internet Service Providers Model based on this point of view. NetZero provides online service to users and derives its income from two sources, advertisers and information buyers. This view is captured by the Hybrid Model graph shown on Figure 14. The Hybrid Model shows that NetZero plays two roles: Seller (selling information and advertisement service) and buyer. NetZero barters to gain the information from end users by providing free Internet access to them. In principle, NetZero and end users play the roles of the buyer and the seller respectively. When NetZero provides services to advertisers, NetZero is an advertisement provider to the buyer (marketer). Therefore NetZero has revenue, $1 (this is what Eisenmann is focused on), flows into its vertex, v12. NetZero also has another source of revenues, $2 (this is what Rappa is focused on and led to the term Infomediary), which comes from the sales of information gathered from the end users. All these revenues are possible because NetZero provides free Internet access service (its SIP) to the end users. Based on the sources of revenue, the graph representation of NetZero includes both the Infomediary component and an online access provider component. But the fact that not all in the Internet Access Providers Model are Infomediary nor all in the Infomediary Model have to be online access providers indicates is in fact a three-prong Direct Exchange Model depicted by Figure 14. Figure 14 could have been interpreted as either model. The graph model thus helps clarify why could have been classified so differently. The difference is not entirely semantic, but due to two different viewpoints, one is revenue-centric and the other one is service-centric. Thus graph approach helps resolve the terminology conflicts of two different authors.

Figure 14: Graph Representation of
Netzero has been categorized as Infomediary Model by Rappa but as Internet Access Providers Model by Eisenmann. Such confusion is due to authors' different viewpoints, revenue-centric vs. service-centric.'s business model is captured by its interaction with three different types of customers, advertisers, information buyers, and end users.

Anatomically, the Hybrid Model graph representing Eisenmann's Internet Access Providers Model as shown in Figure 7A consists of three vertices and three directed edges. The Hybrid Model graph representing Rappa's Infomediary Model as shown in Figure 7B consists of three vertices and four directed edges. In reality the should be represented by Figure 14 which contains four vertices: v12, the prime business actor, has three indegrees (two revenues flows from information buyers and advertisers, and one is valuable information from users) and three outdegrees (free Internet access service to end users, an ad service to advertisers, and information products to information buyers).

Figure 15A: Stage I: Yahoo Model as a startup, a portal provider, provided information absolutely free as a startup.

Applying graph models to evolving IBMs

Evolving IBMs are difficult to classify because of their fluidity. Moreover, many successful Internet businesses employ several models concurrently and constantly adopt new ones to increase flows of revenue and expand customer base in order to survive. Evolution is a very important and common feature of Internet businesses in their early stages. Classifying evolving taxonomy of IBMs is thus a big challenge. In fact, the business models of some dotcoms cited as examples in BERT's IBM categories have already changed and should be recategorized. and are two great examples.'s business model today is very different from when it started as an online book retailer. The flexibility to alter graphs helps capture the evolving phenomena of IBMs. is classified as Advertising Model by Rappa, an Information Brokerage Model by Timmers, and an Online Portals Model by Eisenmann. Yahoo was first created in January 1994, incorporated in March 1995, and went public in April 1996. The core concept of Yahoo! is to be a single place for end users to find useful Web sites. The core concept behind Yahoo! hasn't changed even though it has evolved into a much more complicated business model today, and is still evolving. Yahoo! has at least two distinct groups of customers, non-paying customers (Web end users) and paying customers (companies) that are trying to market services, information, or products (SIP) to end users. Yahoo! started as a pure Gift Model as shown in Figure 15A in 1994. After Yahoo! attracted sufficient numbers of end users to its site, advertisers began to see it as a good place to market their products or services. Therefore Yahoo! evolved from a Gift Model into a Hybrid Model as shown in Figure 15B. Figure 15B is constructed by two basic building blocks, Gift Model (left side of the diagram between v2 and v1) and Direct Exchange Model (right-hand side of diagram between v2 and v1). Yahoo! gains revenue from advertisers who pay a premium for advertisements. Unlike the Type I Indirect Model as shown in Figure 6A, Yahoo! doesn't need to facilitate a successful sale for its paying customers (advertisers) to gain revenue; therefore it is not an Indirect Model. Yahoo! is a Hybrid Model that contains the Gift Model as a core component of its IBM. Today, Yahoo! provides a variety of consumer, marketing, business and enterprise, and premium services. These services or products have been added into Yahoo's business model within less than a decade. Some of them are based on the Direct Exchange Model such as selling digital contents and some of them are derived from the Indirect Model such as Yahoo!Auction. By simply adding the basic Direct Exchange Model and Indirect Model to the Figure 15B, the evolving path of Yahoo! can be easily captured and studied. For example, to capture the sales of digital contents, we simply add another Direct Exchange Model (the component between v2 and v1) to Figure 15B as shown in Figure15C. Yahoo's business today can be a combination of a number of basic GM, DEM, and IM. From Figure 15A to Figure 15C we can see a trend that the number of indegree increases from zero to two, mapping increases in the sources of revenue. The total number of indegree and outdegree increased from one to five which indicates that the complexity of business model of increased as well.

Figure 15B: Stage II: adding ad revenue sells banner ads after attracting sufficient users to its site.

Figure 15C: Stage III: expanding revenue to digital content started expanding its revenue source to sell digital content. Graph represents Yahoo's business model after adding commercial online content.

Applying graph models to synthesize new IBMs

The exciting aspect of this approach is the ability to use graphs to enumerate various business models, some of which could be new. For example, a graph composed of three vertices could have two to six edges. There are a total 20 possible ways to connect three vertices by two to six edges without considering the directions and types of transactions. If directions and transactional types ($ or SIP) are assigned to these edges, many more configurations are possible. If each configuration could be a business model, then one of these combinations could be a new or not yet adopted IBM. For example, could a graph containing three vertices be connected in such a way (see Figure 16) to be considered as a valid business model? Such a business is inconceivable at first glance. But if someone could put it into practice, it could be a new IBM. So far we have yet to find an existing IBM, at least those found in the BERT taxonomies, including evolving ones, that can't be analyzed by the graph approach. Another example of an evolving model is the click-and-mortar model. Figure 17 illustrates one case of this model. In it, the buyer (v1) makes a purchase online but then picks up the product in local store. It can easily be accommodated by using a graphical scheme to capture these evolving phenomena.

Figure 16: A hypothetical business model
An IBM which does not belong to BERT and is created out of one of 20 possible graphs composed of three vertices and two to four edges. Such an IBM may or may not be a valid IBM at all.

Figure 17: Graph of a click-and-brick model
In the rectangle box, the shaded circle represents the established brick-and-mortar store and the white circle represents its online presence.

The final analysis of the BERT taxonomies is summarized in Table 2. Table 2 provides the insight that there is a more general structure in IBM taxonomy than previously realized. We analyzed the dotcom examples provided by BERT and found that many BERT IBMs are Hybrid Models that are assembled by the three basic building blocks: Gift Model, Direct Exchange Model, and Indirect Model. In some cases the same example is classified in different categories. And in some cases the examples in the same category are better represented by different kinds of graphs. Overall it is found that graph representations are completely adequate to analyze all the models proposed by BERT. Thanks to this summary in Table 2, we are confident that our approach is useful in analyzing and classifying IBMs.

Future applications of graph models

When applied properly, the three basic types of graph models — GM, DEM and IM — could unambiguously identify a business model or untangle the meaning of a business model. Earlier in this paper, we summarized how these graphs could be used to analyze BERT taxonomies. This collection of graph models should not be treated as taxonomy per se. Graphs are too abstract to be a practical taxonomy. Instead, they can be viewed as archetypes of IBMs that could be used as a guideline to construct a new taxonomy besides analyzing the BERT models. The current treatment of graphs quickly expounds (from the primary business actor's point of view) business actors and transactions involved in a business model. With these graphic vehicles, an audience can quickly understand the nature of a BERT taxonomic model.

The present four high-level graph models can be differentiated into finer detail by defining (1) types of products, services, and information (physical goods, digital contents, knowledge); (2) the interaction pattern between primary actor and its interacting business actors (one-to-one, one-to-many, many-to-one, many-to-many); (3) scale, method, time, and space of business transactions; (4) types of market environments (B-to-B, B-to-C, or C-to-C); (5) forms of price-discovery mechanisms (open market, sell-side auctions, buy-side auctions, or exchanges); and, (6) value chain proposition or value-creation processes. It is neither the intention nor in the scope of this paper to recognize these subtle differentiations. We see these options as future lines of research. By supplying the specific types of products, actors, and transactions, one can create subcategories of graph models.

Table 2 shows that some BERT IBMs could be analyzed by a graphic representation of the Direct Exchange Model, meaning they all share the same property of direct exchange. For some of them, the differences are semantic, for instance, Rappa's Merchant Model is practically identical to Timmers' e-shop and Eisenmann's Online Retailers. For others the difference rests in the specifications of the types of products or customers addressed. For instance, three of Rappa's models — Merchant, Subscription and Utility — all have characteristics of the Direct Exchange Model (see Table 2), but were named based mainly on the manner of payment and type of products. However, the Merchant Model sells physical products or digital products (bits) based on list prices per order; the Subscription Model sells high-value information based on periodic payments; and, the Utility Model sells information by metering bits (micro-payment). On the other hand, Eisenmann's descriptors — Internet Access Providers, Online Content Providers, Online Retailers, Network Utility Providers, and Application Service Providers — is more toward the types of services (Internet Access, Applications Service), products (physical product), and customers (Network Utility). It is interesting to point out that graph models help us detect these two distinct ways of naming IBMs. Bambury falls into the same pattern as Eisenmann. But Timmers' models are based more on value chain. In fact, more IBMs than BERT taxonomies could have been defined based on specific types of SIP (services, information, and products), types or characteristics of actors, and the exact manner and timing of SIP delivery. When all these factors are considered with graph models, it may be possible to create a taxonomy that can attain universal acceptance or appeal.




The emergence of dotcoms in the last decade provided many new business models on the virtual landscape. With so many co-existing models, there has been a need to classify them into a well-defined taxonomy. Currently there exist several models of IBM taxonomies. Not surprisingly, these models are very different from each other because of their diverse classification schemes and different view points. It is difficult to judge which taxonomy truly maps well to reality. In addition, none of the current taxonomies can account for IBM models that are still evolving. Fortunately, it appears that graph theory could be applied to IBM taxonomy and facilitate its analysis. A graph is a mathematical structure consisting of vertices connected by edges. With vertices representing business agents and edges representing business transactions, most IBMs could be represented by a set of simple graphs. In graph taxonomy, IBMs are analyzed by (1) Gift Model; (2) Direct Exchange Model; (3) Indirect Model; and, (4) Hybrid Models. It is found that this set of IBM graphs reproduce all IBMs contained in the current Bambury, Eisenmann, Rappa, and Timmers taxonomies under investigation. The graph models help explain the classification principles in operation for BERT models. It is also found that graph models are capable of accommodating evolving IBMs and even predicting new models.

It is quite a surprise that such a complex system of Internet business taxonomy could be nicely analyzed using graphs, a mathematical tool developed by Euler some two centuries ago. The graph is capable of qualitative analysis. Yet we found that a qualitative application of graphs provides sufficient detail to sort out various Internet business models. We believe that we have established that graphs are a useful tool to analyze IBMs, and may serve as a systematic way to generate a universal IBM taxonomy. When applied to the various BERT schemes, graph analysis can unambiguously sort out similarities and differences of these models. The result of such analysis is summarized in Table 2. We believe that we have shed some light on a potential theoretical framework for a systematic analysis of Internet business models. More work is needed quantitatively which may shed light on why some models are more successful than others. End of article


About the Authors

Chiou-Pirng (Ping) Wang is currently an Assistant Professor in the Business Administration Department of College of Business at Albany State University in Albany, Georgia. She is current interested in finding a way to capture the pattern of evolving Internet businesses.
Direct comments on this paper to

Kwaichow Chan is an Associate Professor of Physics at Albany State University whose current interest is to apply graphs to solve a tanglegram series problem and dendritic growth.



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Editorial history

Paper received 30 January 2003; accepted 16 May 2003.

Contents Index

Copyright ©2003, First Monday

Copyright ©2003, Chiou-Pirng Wang

Copyright ©2003, KwaiChow Chan

Analyzing the Taxonomy of Internet Business Models Using Graphs by Chiou-Pirng Wang and KwaiChow Chan
First Monday, volume 8, number 6 (June 2003),