1. Introduction to e-Commerce
Network Theory 101
Dr. Michael D. Featherstone

2. Networks consists of edges and nodes

3. Credibility, Connectiivity and Bandwidth.
Networks 101
From an e-Commerce perspective there are three fundamental elements of Networks.
Credibility, Connectiivity and Bandwidth.

4. Networks 101 What is a Network? Source
In network theory, we focus on relationships: how and why they form; what these ties represent; how different relationships affect behaviors; and how relationships grow and decay over time.
We use mathematics to represent these relationships, and statistics to analyze these relationships (well They do, anyway).
More recently, we have extended to use these tools as a way to understand and anticipate behavior. As such, we can apply formal representations of human interactions from Sociology, the dynamics of markets from Economics, and problems of collective action from Political Science all to the study of network theory.
Although social networks are perhaps the most relevant networks of the moment, there are many kinds of networks, such as information, transportation, and biological networks

5. Networks 101
Centrality is a general measure of how the position of a vertex is within the overall structure of the graph - for example, how influential someone is on Twitter based on how many followers (in-degree) they have. Centrality is among the most basic, but important and commonly encountered measures in network analysis.

6. Networks 101
A concrete measurable pattern of relationships among entities in a social space. Source
Examples:
(1) Social networks among individuals: friendship, advice-seeking, romantic connections, acquaintanceship
(2) “Formal,” contractual relationships among organizations: strategic alliances, buyer-supplier contracts, joint ventures etc.
(3) “Informal” inter-organizational relationships flow through people: director interlocks, employee mobility, social networks that cross organizational boundaries
(4) Affiliations, shared memberships that suggest connections: trade associations, committee memberships, co-authorships etc.

7. The Web is a Complex Network
Graphic view of the Web (by tracing links)
The Web is a Network … Not only that, the Web is complex network… so says Sir Tim Berners-Lee (and just about every other scientist in the world who is doing research on networks or complexity theory).
So let’s take this as a given. The Web is a Complex Network

8. Complex Systems share certain attributes
When scientists speak of complex systems they don't mean systems that are complicated or perplexing in an informal way. The phrase "complex system" has been adopted as a specific technical term.
Complex systems typically have a large number of small parts or components that
interact with similar nearby parts and components (The “long tail” of the power law for example).
These local interactions often lead to the system organizing itself without any master control or external agent being "in charge" (Which would explain why such systems are often referred to as being self-organizing).
Such systems usually form power law distributions.
These self-organized systems are also dynamic systems under constant change.
Short of death or destruction, they do not settle info a final stable "equilibrium" state.
New entities emerge in complex systems.
To the extent these systems react to changes in their environment so as to maintain their integrity, they are known as complex adaptive systems.

9. The Web is a Complex Network
Graphic view of the Web (by tracing links)
Today there are literally dozens of books trying to explain complexity theory. 9

10. Barabasi also identified certain Web characteristics
Research published by scientists at Notre Dame in 1999 indicated that there were fundamental characteristics of most networks, including the Internet and the Web, in that they:
Exhibited rapid and/or consistent growth.
Exhibited a power law distribution.
Exhibited forms of preferential attachment.

11. Rapid Growth
Netcraft's latest Web survey found 101,435,253 websites in November Not all of these sites are live: some are "parked" domains, while others are abandoned weblogs that haven't been updated in ages. But even if only half the sites are maintained, there are still more than 100 M sites that people pay to keep running.
As the chart shows, the number of Websites has experienced three growth stages:
: Explosive growth, at a rate of 850% per year.
: Rapid growth, at a rate of 150% per year.
: Maturing growth, at a rate of 25% per year.

12. Power Law Distribution
Power laws as related to websites may be verbally represented as:
a very few sites that rank very high in the number of inbound links;
a larger number of sites with close to median numbers of inbound links;
a great number of sites with very few inbound links.

13. Preferential Attachment
Explanations of ‘Preferential Attachment’ remain unresolved
Some scientists suggest a ‘Rich get richer’ phenomenon.
Some scientist have noted that the ‘First Adaptor’ advantage explains preferential attachment.
Others have suggested that the emergence of new ‘species’ of businesses on the Web may explain preferential attachment.

14. This Concludes the Network Theory Presentation
Thank you for your attention