Networking Fundamentals & Network Modeling

Hub and Connectors

Connectors are an extremely important component of our social network. They create trends and fashions, make important deals, spread fads, or help launch a new business. Connectors are nodes with an anomalously large number of links.

The Internet is the Ultimate freedom of speech. When your views are published, it will be available instantaneously available to anyone around the world with an Internet connection. With the billions of webpages on the web, the question is -- will anybody notice it?

In order to be read, you have to be visible. On the web, the measure of visibility is the number of links. The more incoming links pointing to your webpage, the more visible it is. The average Webpage only has about five to seven links, each pointing to one of the billion pages out there. The likelihood that a typical document is linked to your Webpage is practically zero.

Just as in Society a few connections know an unusually large number of people, and the Internet is dominated by a few highly connected nodes, or hubs. These hubs, such as Yahoo! and Google are extremely visible. In a collective manner, we somehow create hubs, Websites to which everyone links. Compared to these hubs, everyone is invisible. Some pages linked to one or two documents do not exist and even search engines are biased against them, ignoring them as they crawl the web looking for the hottest new sites.

Hubs dominate the structure of all networks which they are present, making them look like small worlds. With unusually large number of links to large number of nodes, hubs create short paths between any two nodes in the system. From the perspective of the hub, the world is tiny. (For Google, reaching webpages are often two to three clicks away)

The 80/20 Rule

Pareto's Law or principle, known also as the 80/20 rule, has been turned into the Murphy's Law of management: 80 percent of profits are produced by 20 percent of the employees, 80 percent of the problems are produced by 20 percent of the consumers, 80 percent of the decisions are made during 20 percent of the meeting time, and so on. Similarly, we can use it to describe the phenomenon that 80 percent of the links connect to 20 percent of the Webpages.

The Rich get Richer

The initial network model start on two simple and often disregarded assumptions; the number of nodes is fixed and remain unchanged throughout the network's life, all nodes are equivalent. With the discovery of hubs, and the power laws that describe them, we need to abandon these assumptions.

On the World Wide Web, even for searches on Google with the keyword "news", there are 100,000,000 hits. How do we pick one? The random network models tell us to select randomly, however no one ever does this. Without giving much thought we may pick BBC.com or CNN.com and unconsciously, we prefer to link hubs. The better known they are, the links point to them. The more links they attract, the easier it is to find them on the Web as we are more familiar with them. We all have this unconscious bias, linking with higher probability to the nodes we know, which are inevitably the more connected nodes of the Web. We prefer hubs.

Preferential attachment rules in many different networks. In Hollywood, the producer whose job is to make the movie profitable know that stars sell movies. Thus casting is determined by two competing factors: the match between the actor and the role, and the actor's popularity. The more movie the actor has made, the higher the probability he gets casted by the producer.

Winner Takes All

Nodes compete for connections because links represent survival in an interconnected world. In most cases, this competition is overt, as when companies compete for consumers, actors strive for opportunities to perform, people vie for social links. In a winner takes all scenario, competition leads to a scale free topology. Most real networks belong to this category, and the winner shares the spotlight with continuous hierarchy of hubs. Networks are competitive systems that fight fiercely for links. Like it or not, we are all part of a complex competitive game.

.... To be Continued

-- Robin Low