Abstract
The analysis of biological networks allows the understanding of many biological processes, including the structure, function, interaction and evolutionary relationships of their components. One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are interested in searching and inferring network motifs in a class of biological networks that can be represented by vertex-colored graphs. We show the computational complexity for many problems related to colorful topological motifs and present efficient algorithms for special cases. A colorful motif can be represented by a graph in which each vertex has a different color. We also present a probabilistic strategy to detect highly frequent motifs in vertex-colored graphs. Experiments on real data sets show that our algorithms are very competitive both in efficiency and in quality of the solutions.
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Notes
Notice that this problem was proposed previously and was shown W[1]-hard Marx (2007). Despite of that, our NP-completeness proof is simple and straightforward.
Our implementation, including documentation, compilation parameters and libraries used, can be found at http://simbio.wp.facom.ufms.br.
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We thank the anonymous reviewers for their careful reading of the manuscript and their many insightful comments and suggestions.
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Rubert, D.P., Araujo, E., Stefanes, M.A. et al. Searching and inferring colorful topological motifs in vertex-colored graphs. J Comb Optim 40, 379–411 (2020). https://doi.org/10.1007/s10878-020-00590-4
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DOI: https://doi.org/10.1007/s10878-020-00590-4