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arXiv · 1308.3380

Vertex-pursuit in random directed acyclic graphs

Anthony Bonato·Dieter Mitsche·P. Pralat
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Abstract

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. The minimum number of such agents required to block the intruder is called the green number. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage and the green number is analyzed in stochastic DAGs in both the cases of a regular and power law degree sequence. For each such sequence, we give asymptotic bounds (and in certain instances, precise values) for the green number.

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Anthony Bonato, Dieter Mitsche, P. Pralat. 2013-08-15. Vertex-pursuit in random directed acyclic graphs. https://arxiv.org/abs/1308.3380

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