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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n5zrklrhlzhtdorf4rk4rmeo3i" style="color: black;">BMC Bioinformatics</a>
Network methods are increasingly used to represent the interactions of genes and/ or proteins. Genes or proteins that are directly linked may have a similar biological function or may be part of the same biological pathway. Since the information on the connection (adjacency) between 2 nodes may be noisy or incomplete, it can be desirable to consider alternative measures of pairwise interconnectedness. Here we study a class of measures that are proportional to the number of neighbors that a pair<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/1471-2105-8-22">doi:10.1186/1471-2105-8-22</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/17250769">pmid:17250769</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC1797055/">pmcid:PMC1797055</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i36lg3rhafgj3msrkuvbg5p5la">fatcat:i36lg3rhafgj3msrkuvbg5p5la</a> </span>
more »... of nodes share in common. For example, the topological overlap measure by Ravasz et al.  can be interpreted as a measure of agreement between the m = 1 step neighborhoods of 2 nodes. Several studies have shown that two proteins having a higher topological overlap are more likely to belong to the same functional class than proteins having a lower topological overlap. Here we address the question whether a measure of topological overlap based on higher-order neighborhoods could give rise to a more robust and sensitive measure of interconnectedness. Results: We generalize the topological overlap measure from m = 1 step neighborhoods to m ≥ 2 step neighborhoods. This allows us to define the m-th order generalized topological overlap measure (GTOM) by (i) counting the number of m-step neighbors that a pair of nodes share and (ii) normalizing it to take a value between 0 and 1. Using theoretical arguments, a yeast coexpression network application, and a fly protein network application, we illustrate the usefulness of the proposed measure for module detection and gene neighborhood analysis. Conclusion: Topological overlap can serve as an important filter to counter the effects of spurious or missing connections between network nodes. The m-th order topological overlap measure allows one to trade-off sensitivity versus specificity when it comes to defining pairwise interconnectedness and network modules.
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