Power Law Networks

Accounting for Popularity

Although the organization and popularity of online social networks can seem somewhat random, the concept of power laws accounts for this acceleration in popularity. Power laws explain how certain networks gain large followings and garner spikes in activity over other sites; they receive a disproportionate number of hits. Rather than following a traditional bell curve distribution, networks that operate by a power law begin at their maximum value and decay slowly in value. Because power law networks decay slower than bell curve networks, smaller hub networks can form during these decreases. These hubs account for various networks that serve the long tail of interests online, distributing links along these networks without the strength of link ties seen in the power law network.

As scale-free networks, power law networks are not bound by growth or acceleration like other networks. In theory, this means that they can grow exponentially without constraints. Such growth is measured by the amount of inbound links, directed by other networks. The number of inbound links are used to measure this activity, but other attributes, such as number of participating users, number of postings, and quantity of content, can also be indicative of a power law network.

Power laws account for the popularity of certain Websites, which are at the maximum value of the long tail. The tail spikes in popularity, with each subsequent network sloping downward as it loses value related to the size of the power law. Each point below the power law network becomes smaller by about half the size of the original network. The spike in the power law network is pronounced, while the other networks can slope low and outward across the chart, marking long-tail networks. While the culmination of all of the long-tail sites might garner more links, participants, and content than the power law network, these long-tail networks' lack of concentrated participation makes them weaker in power.

These power law networks represent a critical mass of links, which may equate to large numbers of participants and content. However, such causality is not necessarily a given, as there could be various reasons why power law networks are linked more often than weaker sites. Some researchers relate this linking to the 80/20 rule, in that 80 percent of participants are on 20 percent of the systems. At the top of this 20 percent is the power law network. The network directly below this network can grow exponentially, but the power law network is the small world phenomenon network that can grow infinitely larger.

The top sites, whether they are social networks, blogs, or other systems, typically contain the highest number of inbound links. This concentration allows these networks to gain larger market share, content distribution, or whatever other goals the system leaders are after. Such a mass of links can allow this network to expand outward, subsuming other networks and gaining larger market share. Mathematically, power laws are polynomials with either one or more variables. If the polynomial is a power law, it will have a scale invariance. Essentially, the value multiplies itself over and over such that it will graph a sudden increase in the relationship between these quantities to show the power of a given object, such as the ranking of Website popularity.

...