Branching process approach for Boolean bipartite networks of metabolic reactions

Abstract

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR logic gates. We reduce the bipartite network into a unipartite network by integrating out OR gates, and obtain the effective branching ratio for the remaining AND gates. Then the standard BP approach is applied to the reduced network, and the avalanche size distribution is obtained. We test the BP results with simulations on the model networks and two microbial metabolic networks, demonstrating the usefulness of the BP approach.

References in corpus (11)

• Epidemic spreading in scale-free networks
• The large-scale organization of metabolic networks
• Random graphs with arbitrary degree distributions and their applications
• Resilience of the Internet to random breakdowns
• Sandpile on Scale-Free Networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Multiplexity-facilitated cascades in networks
• Accuracy of Mean-Field Theory for Dynamics on Real-World Networks
• Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
• Spreading of infectious diseases on heterogeneous populations: multi-type network approach
• Scale-free random branching tree in supercritical phase

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