Community detection in directed acyclic graphs

Leo Speidel; Taro Takaguchi; Naoki Masuda

doi:10.1140/epjb/e2015-60226-y

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The European Physical Journal B

August 2015, 88:203

Community detection in directed acyclic graphs

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Leo Speidel
Taro Takaguchi
Naoki MasudaEmail author

Open Access

Regular Article

First Online:: 10 August 2015

Received:: 20 March 2015
Revised:: 27 June 2015

DOI: 10.1140/epjb/e2015-60226-y

Cite this article as:: Speidel, L., Takaguchi, T. & Masuda, N. Eur. Phys. J. B (2015) 88: 203. doi:10.1140/epjb/e2015-60226-y

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Topical issue: Temporal Network Theory and Applications

Abstract

Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement a spectral method to approximately maximize the proposed modularity measure and test the method on citation networks and other DAGs. We find that the attained values of the modularity for DAGs are similar for partitions that we obtain by maximizing the proposed modularity (designed for DAGs), the modularity for undirected networks and that for general directed networks. In other words, if we neglect the order imposed on nodes (and the direction of links) in a given DAG and maximize the conventional modularity measure, the obtained partition is close to the optimal one in the sense of the modularity for DAGs.

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Community detection in directed acyclic graphs

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