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Center for Nonlinear Studies |
Graphs are a popular way to model interactions in a wide range of applications, including rapidly-growing data drawn from natural, social, and information sciences. However, one significant challenge in analyzing large complex networks has been understanding the "intermediate-scale" structure, i.e., those properties not captured by metrics which are very local (e.g., clustering coefficient) or very global (e.g., degree distribution). It is often this structure which governs the dynamic evolution of the network and the behavior of diffusion-like processes on it. Although there is a large body of empirical evidence suggesting that complex networks have "tree-like" properties at intermediate to large size-scales (e.g., hierarchical structures in biology, hyperbolic routing in the Internet, and core-periphery behavior in social networks), it remains a challenge to quantify and take algorithmic advantage of this structure in many data analysis applications. In this talk, we describe recent empirical and theoretical results aimed at integrating techniques from structural graph theory (tree decompositions and minors), metric embedding theory (Gromov hyperbolicity), and scalable heuristics (k-core decompositions) into scalable and robust tools for extracting meaningful tree-like structure from large informatics networks, including some surprising parameter relationships and computational results showing successes and failings when applied to real world data.
Host: Nathan Lemons