Abstract
Complex networks can store information in form of periodic orbits (cycles) existing in the network. This cycle-based approach although computationally intensive, it provided us with useful information about the behavior and connectivity of the network. Social networks in most works are treated like any complex network with minimal sociological features modeled. Hence the cycle distribution will suggest the true capacity of this social network to store information. Counting cycles in complex networks is an NP-hard problem. This work proposed an efficient algorithm based on statistical mechanical based Belief Propagation (BP) algorithm to compute cycles in different complex networks using a phenomenological Gaussian distribution of cycles. The enhanced BP algorithm was applied and tested on different networks and the results showed that our model accurately approximated the cycles distribution of those networks, and that the best accuracy was obtained for the random network. In addition, a clear improvement was achieved in the cycles computation time. In some cases the execution time was reduced by up to 88 % compared to the original BP algorithm.
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Sorkhoh, I., Mahdi, K.A. & Safar, M. Estimation algorithm for counting periodic orbits in complex social networks. Inf Syst Front 15, 193–202 (2013). https://doi.org/10.1007/s10796-012-9366-9
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DOI: https://doi.org/10.1007/s10796-012-9366-9