Date and LocationJun 02, 2015 - 4:00pm
A large stream of research spurred by the work of Mark Newman has developed methods for the detection of community structure, defined as the appearance of densely connected groups of vertices (relative to a null model), with only sparser connections between groups. Two points (related to each other) that have been noted in a recent comprehensive review are that (a) research on the community structure of multilayer networks is in need of much further development, and (b) much more work is needed on mesoscale features other than community structure, both in single-layer and multilayer networks.
I suggest that a particular approach to community detection in the case of networks of directed ties leads naturally to a broadening of the kinds of patterns that are of interest to analysts who employ leading eigenvector community detection algorithms. My talk presents, not a thoroughly new or general method, but rather some hopefully novel insight into directed networks as a distinctive kind of multilayer network, as well as into how multiple directed (and undirected) networks can be modeled within a single analysis based on a straightforward extension of leading eigenvector community detection. A suitable version of the modularity matrix for this task will in general not yield community structure, but rather a pattern in which each identified set in a partition of nodes may in principle have unusually dense (or sparse) connections with every other such set, a pattern that may be distinctive with respect to each of the multiple networks analyzed. This work thus uses fundamental ideas from the community detection literature to move beyond a sole reliance on the pattern of community structure, and thus it enlarges the toolbox of mesoscale patterns available to analysts of multilayer networks. I illustrate the suggested approach by means of analyses of several well-known multilayer networks, including appropriate assessments of model fit.
Host: Prof. John Mohr, Sociology