The map equation

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash application, see http://www.tp.umu.se/~rosvall/livemod/mapequation

Decomposition of the Google pagerank and optimal linking strategy

We provide the analysis of the Google PageRank from the perspective of the Markov Chain Theory. First we study the Google PageRank for a Web that can be decomposed into several connected components which do not have any links to each other. We show that in order to determine the Google PageRank for a completely decomposable Web, it is sufficient to compute a subPageRank for each of the connected components separately. Then, we study incentives for the Web users to form connected components. In particular, we show that there exists an optimal linking strategy that benefits a user with links inside its Web community and on the other hand inappropriate links penalize the Web users and their Web communities. \u

University of Twente at the TREC 2007 Enterprise Track : modeling relevance propagation for the expert search task

This paper describes several approaches which we used for the expert search task of the TREC 2007 Enterprise track.\ud We studied several methods of relevance propagation from documents to related candidate experts. Instead of one-step propagation from documents to directly related candidates, used by many systems in the previous years, we do not limit the relevance flow and disseminate it further through mutual documents-candidates connections. We model relevance propagation using random walk principles, or in formal terms, discrete Markov processes. We experiment with\ud innite and nite number of propagation steps. We also demonstrate how additional information, namely hyperlinks among documents, organizational structure of the enterprise and relevance feedback may be utilized by the presented techniques