Winners don’t take all: Characterizing the competition for links on the web

By Pennock, Flake, Lawrence, Glover, and Giles (2002)

ABSTRACT
As a whole, the World Wide Web displays a striking ‘‘rich get richer’’ behavior, with a relatively small number of sites receiving a disproportionately large share of hyperlink references and traffic. However, hidden in this skewed global distribution, we discover a qualitatively different and considerably less biased link distribution among subcategories of pages—for example, among all university homepages or all newspaper homepages. Although the connectivity distribution over the entire web is close to a pure power law, we find that the distribution within specific categories is typically unimodal on a log scale, with the location of the mode, and thus the extent of the rich get richer phenomenon, varying across different categories. Similar distributions occur in many other naturally occurring networks, including research paper citations, movie actor collaborations, and United States power grid connections. A simple generative model, incorporating a mixture of preferential and uniform attachment, quantifies the degree to which the rich nodes grow richer, and how new (and poorly connected) nodes can compete. The model accurately accounts for the true connectivity distributions of category-specific web pages, the web as a whole, and other social networks.

Paper here

Celebrity in social networks: how can we avoid the power law distribution?

By Ben Werdmuller

“In any information ecosystem, there is an observable tendency for a few sources on a topic – be they journals, websites or people – to have a massive following, a significantly smaller number to have a medium number of followers, and then a final, largest group to have a much smaller number of regular readers. This can be witnessed in the Technorati Top 100: the top 100 blogs range from around 80,900 unique links to 4,900 (quite a decrease), yet Technorati track 26.6 million sites. If the downward link trend continues across all 26.6 million, most weblogs have at most one a handful of links – and therefore a correspondingly small number of readers. I’ve been wondering for a while how best to verbalise this…”

complete article here