Abstract
The prevalence of select substructures is an indicator of network effects in applications such as social network analysis and systems biology. Moreover, subgraph statistics are pervasive in stochastic network models, and they need to be assessed repeatedly in MCMC sampling and estimation algorithms. We present a new approach to count all induced and non-induced 4-node subgraphs (the quad census) on a per-node and per-edge basis, complete with a separation into their non-automorphic roles in these subgraphs. It is the first approach to do so in a unified manner, and is based on only a clique-listing subroutine. Computational experiments indicate that, despite its simplicity, the approach outperforms previous, less general approaches.
We gratefully acknowledge financial support from Deutsche Forschungsgemeinschaft under grant Br 2158/11-1.
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Ortmann, M., Brandes, U. (2016). Quad Census Computation: Simple, Efficient, and Orbit-Aware. In: Wierzbicki, A., Brandes, U., Schweitzer, F., Pedreschi, D. (eds) Advances in Network Science. NetSci-X 2016. Lecture Notes in Computer Science(), vol 9564. Springer, Cham. https://doi.org/10.1007/978-3-319-28361-6_1
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