Algorithms for estimating relative importance in networks

Large and complex graphs representing relationships among sets of entities are an increasingly common focus of interest in data analysis---examples include social networks, Web graphs, telecommunication networks, and biological networks. In interactive analysis of such data a natural query is "which entities are most important in the network relative to a particular individual or set of individuals?" We investigate the problem of answering such queries in this paper, focusing in particular on defining and computing the importance of nodes in a graph relative to one or more root nodes. We define a general framework and a number of different algorithms, building on ideas from social networks, graph theory, Markov models, and Web graph analysis. We experimentally evaluate the different properties of these algorithms on toy graphs and demonstrate how our approach can be used to study relative importance in real-world networks including a network of interactions among September 11th terrorists, a network of collaborative research in biotechnology among companies and universities, and a network of co-authorship relationships among computer science researchers.