Vertex-Pursuit in hierarchical social networks

Authors:
A. Bonato;D. Mitsche;P. Prałat
Affiliations:
Department of Mathematics, Ryerson University, Toronto, Canada;Department of Mathematics, Ryerson University, Toronto, Canada;Department of Mathematics, Ryerson University, Toronto, Canada
Venue:
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Year:
2012

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Abstract

Hierarchical social networks appear in a variety of contexts, such as the on-line social network Twitter, the social organization of companies, and terrorist networks. We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage is analyzed rigorously in stochastic DAGs in both the cases of a regular and power law degree sequence.