Ortmann M, Brandes U. Efficient orbit-aware triad and quad census in directed and undirected graphs.
Appl Netw Sci 2017;
2:13. [PMID:
30443568 PMCID:
PMC6214268 DOI:
10.1007/s41109-017-0027-2]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Accepted: 04/20/2017] [Indexed: 06/09/2023]
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 four-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. By way of the more presentable triad census, we additionally show how to extend the quad census to directed graphs. As a byproduct we obtain the asymptotically fastest triad census algorithm to date.
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