Hodge Decomposition of Information Flow on Complex Networks

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8th International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)
Yuuya Fujiki1, Taichi Haruna1
1: Kobe University

    Decomposition of information flow associated with random threshold network dynamics on random networks with specified degree distributions is studied by numerical simulation. Combinatorial Hodge theory enables us to orthogonally decompose information flow into gradient (unidirectional acyclic flow), harmonic (global circular flow) and curl (local circular flow) components. We show that in-degree distribution has little influence on the relative strength of the circular component (harmonic plus curl) while out-degree distributions with longer tail suppress it. We discuss an implication of this finding on the topology of real-world gene regulatory networks.