Deokjae Lee, K. -I. Goh, B. Kahng
The branching process (BP) approach has been successful in understanding the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks in which nodes are all of the same type. Here, we develop the BP approach for a particular bipartite Boolean network, composed of logic OR and AND gates, which is motivated to understand the avalanche dynamics in metabolic networks. We reduce the bipartite to a unipartite network by renormalizing the OR gates, and obtain an effective branching ratio for the AND gates. Then the standard BP approach is applied to the reduced unipartite network, and the avalanche size distribution is obtained. We also test the analytic result with simulations on a couple of metabolic networks in real world. They are in reasonable agreement with each other.
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http://arxiv.org/abs/1203.5574
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