Document Zbl 1499.91076

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In this article, due to lots of real-life and artificial networks are built from series of simple and small groups (components), we discuss some interesting and helpful network-operation to generate more realistic network models. In view of community structure (modular topology), we present a class of sparse network models $N(t, m)$. At the moment, we capture the fact the $N(t, 4)$ has not only scale-free feature, which means that the probability that a randomly selected vertex with degree $k$ decays as a power-law, following $P(k) \sim k^{-\gamma}$, where $\gamma$ is the degree exponent, but also small-world property, which indicates that the typical distance between two uniform randomly chosen vertices grows proportionally to logarithm of the order of $N(t, 4)$, namely, relatively shorter diameter and lower average path length, simultaneously displays higher clustering coefficient. Next, as a new topological parameter correlating to reliability, synchronization capability and diffusion properties of networks, the number of spanning trees over a network is studied in more detail, an exact analytical solution for the number of spanning trees of the $N(t, 4)$ is obtained. Based on the network-operation, part hub-vertex linking with each other will be helpful for structuring various network models and investigating the rules related with real-life networks.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7544995">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A91D30" title="MSC2020">91D30</a> </td> <td class="space"> Social networks; opinion dynamics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B10" title="MSC2020">90B10</a> </td> <td class="space"> Deterministic network models in operations research </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anetwork-operation">network-operation</a>; <a href="/?q=ut%3Ascale-free+feature">scale-free feature</a>; <a href="/?q=ut%3Asmall-world+property">small-world property</a>; <a href="/?q=ut%3Anumber+of+spanning+trees">number of spanning trees</a>; <a href="/?q=ut%3Acommunity+structure">community structure</a>; <a href="/?q=ut%3Anetwork+models">network models</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1499.91076" data-ciurl="/ci/07544995" data-biburl="/bibtex/07544995.bib" data-amsurl="/amsrefs/07544995.bib" data-xmlurl="/xml/07544995.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07544995.pdf" title="Zbl 1499.91076 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.physa.2017.04.135" aria-label="DOI for “The relations between network-operation and topological-property in a scale-free and small-world network with community structure”" title="10.1016/j.physa.2017.04.135">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Huberman, B. 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