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diff --git a/doc/html/mammult_docsu35.html b/doc/html/mammult_docsu35.html new file mode 100644 index 0000000..7bac046 --- /dev/null +++ b/doc/html/mammult_docsu35.html @@ -0,0 +1,140 @@ +<!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 fit_knn</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. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch2.html" >next</a>] [<a +href="mammult_docsu34.html" >prev</a>] [<a +href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a +href="#tailmammult_docsu35.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x39-380001.2.3"></a><span +class="cmtt-10x-x-109">fit</span><span +class="cmtt-10x-x-109">_knn</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">fit</span><span +class="cmbx-10x-x-109">_knn </span>- power-law fit of the inter-layer degree correlation function. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">fit</span><span +class="cmbx-10x-x-109">_knn </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">filein</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">alpha</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" > Perform a power-law fit of the inter-layer degree correlation function: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc11x.png" alt="-- 1 ∑ +q(k) = --- q′P (q′|k) + Nq q′ +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > where <span +class="cmmi-10x-x-109">k </span>is the degree of a node on layer 1, <span +class="cmmi-10x-x-109">q </span>is the degree on layer 2 and +<span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">q</span><span +class="cmsy-10x-x-109">|</span><span +class="cmmi-10x-x-109">k</span>) is the probability that a node with degree <span +class="cmmi-10x-x-109">k </span>on layer 1 has degree <span +class="cmmi-10x-x-109">q </span>on +layer 2. The program assumes that <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) can be written in the form <span +class="cmmi-10x-x-109">ak</span><sup><span +class="cmmi-8">b</span></sup>, and +computes the two parameters <span +class="cmmi-10x-x-109">a </span>and <span +class="cmmi-10x-x-109">b </span>through a linear fit of the log-log plot of +<span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>). +<!--l. 37--><p class="indent" > The input file <span +class="cmti-10x-x-109">filein </span>contains a list of lines in the format: +<!--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>is the degree of node <span +class="cmmi-10x-x-109">i </span>at layer 1 and <span +class="cmti-10x-x-109">qi </span>is the degree of node <span +class="cmmi-10x-x-109">i </span>at +layer 2. +<!--l. 37--><p class="indent" > The second parameter <span +class="cmti-10x-x-109">alpha </span>is the ratio of the progression used to generate +the exponentially-distributed bins for the log-log plot. Typical values of <span +class="cmti-10x-x-109">alpha </span>are +between 1<span +class="cmmi-10x-x-109">.</span>1 and 2<span +class="cmmi-10x-x-109">.</span>0. +<!--l. 37--><p class="indent" > N.B.: The exponent <span +class="cmmi-10x-x-109">b </span>computed with this method is known to be +inaccurate. + + + +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 43--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the values of the parameters <span +class="cmmi-10x-x-109">a </span>and <span +class="cmmi-10x-x-109">b </span>of the +power-law fit <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) = <span +class="cmmi-10x-x-109">ak</span><sup><span +class="cmmi-8">b</span></sup>. +<!--l. 50--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 50--><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. 50--><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. 50--><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. 50--><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. 50--><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. 50--><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. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch2.html" >next</a>] [<a +href="mammult_docsu34.html" >prev</a>] [<a +href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a +href="mammult_docsu35.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div> +<!--l. 208--><p class="indent" > <a + id="tailmammult_docsu35.html"></a> +</body></html> |