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| author | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
|---|---|---|
| committer | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
| commit | a86962cbfd0321387c920a04188512d0de2f3036 (patch) | |
| tree | b6c0d31342f7af9d605ee83cfffe251554a307d4 /doc/html/mammult_docsu34.html | |
| parent | df8386f75b0538075d72d52693836bb8878f505b (diff) | |
First commit of MAMMULT documentation
Diffstat (limited to 'doc/html/mammult_docsu34.html')
| -rw-r--r-- | doc/html/mammult_docsu34.html | 164 |
1 files changed, 164 insertions, 0 deletions
diff --git a/doc/html/mammult_docsu34.html b/doc/html/mammult_docsu34.html new file mode 100644 index 0000000..ccd8b5a --- /dev/null +++ b/doc/html/mammult_docsu34.html @@ -0,0 +1,164 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.3.0 knn_q_from_degrees.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu35.html" >next</a>] [<a +href="mammult_docsu33.html" >prev</a>] [<a +href="mammult_docsu33.html#tailmammult_docsu33.html" >prev-tail</a>] [<a +href="#tailmammult_docsu34.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x38-370001.2.3"></a><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_degrees.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_degrees.py </span>- compute the inter-layer degree-degree +correlation function. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_degrees.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">filein</span><span +class="cmmi-10x-x-109">></span> +<!--l. 37--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 37--><p class="indent" > Compute the inter-layer degree correlation functions for two layers of a +multiplex, using the degrees of the nodes specified in the input file. The format of +the input file is as follows +<!--l. 37--><p class="indent" >   <span +class="cmti-10x-x-109">ki qi</span> +<!--l. 37--><p class="indent" > where <span +class="cmti-10x-x-109">ki </span>and <span +class="cmti-10x-x-109">qi </span>are, respectively, the degree at layer 1 and the degree at layer +2 of node <span +class="cmti-10x-x-109">i</span>. +<!--l. 37--><p class="indent" > If we consider two layers of a multiplex, and we denote by <span +class="cmmi-10x-x-109">k </span>the degree +of a node on the first layer and by <span +class="cmmi-10x-x-109">q </span>the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc9x.png" alt="k(q) = -1-∑ k′P (k′|q) + Nk ′ + k +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > where <span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′|</span><span +class="cmmi-10x-x-109">q</span>) is the probability that a node with degree <span +class="cmmi-10x-x-109">q </span>on the second +layer has degree equal to <span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′ </span>on the first layer, and <span +class="cmmi-10x-x-109">N</span><sub><span +class="cmmi-8">k</span></sub> is the number of +nodes with degree <span +class="cmmi-10x-x-109">k </span>on the first layer. The quantity <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) is the expected +degree at layer 1 of node that have degree equal to <span +class="cmmi-10x-x-109">q </span>on layer 2. The dual + + + +quantity: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc10x.png" alt=" ∑ +q(k) = -1- q′P (q′|k) + Nq q′ +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > is the average degree on layer 2 of nodes having degree <span +class="cmmi-10x-x-109">k </span>on layer +1. +<!--l. 57--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 57--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 57--><p class="indent" >   <span +class="cmti-10x-x-109">k </span><span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) +<!--l. 57--><p class="indent" > where <span +class="cmti-10x-x-109">k </span>is the degree on layer 1 and <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of +nodes having degree equal to <span +class="cmmi-10x-x-109">k </span>on layer 1. +<!--l. 57--><p class="indent" > The program also prints on <span +class="cmtt-10x-x-109">stderr </span>a list of lines in the format: +<!--l. 57--><p class="indent" >   <span +class="cmti-10x-x-109">q </span><span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) +<!--l. 57--><p class="indent" > where <span +class="cmti-10x-x-109">q </span>is the degree on layer 2 and <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) is the average degree on layer 1 of +nodes having degree equal to <span +class="cmmi-10x-x-109">q </span>on layer 2. +<!--l. 64--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu35.html" >next</a>] [<a +href="mammult_docsu33.html" >prev</a>] [<a +href="mammult_docsu33.html#tailmammult_docsu33.html" >prev-tail</a>] [<a +href="mammult_docsu34.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu34.html"></a> +</body></html> |