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134 lines
6.1 KiB
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<head><title>1.1.3.0 overlap_degree.py</title>
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<meta name="date" content="2015-10-19 17:14:00">
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<h5 class="subsubsectionHead"><a
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id="x19-180001.1.3"></a><span
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class="cmtt-10x-x-109">overlap</span><span
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class="cmtt-10x-x-109">_degree.py</span></h5>
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<!--l. 3--><p class="noindent" ><span
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class="cmbx-10x-x-109">NAME</span>
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<!--l. 3--><p class="indent" > <span
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class="cmbx-10x-x-109">overlap</span><span
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class="cmbx-10x-x-109">_degree.py </span>- compute the total (overlapping) degree of all the nodes
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of a multiplex and the corresponding Z-score.
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<!--l. 3--><p class="noindent" ><span
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class="cmbx-10x-x-109">SYNOPSYS</span>
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<!--l. 3--><p class="indent" > <span
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class="cmbx-10x-x-109">overlap</span><span
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class="cmbx-10x-x-109">_degree.py </span><span
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class="cmmi-10x-x-109"><</span><span
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class="cmitt-10x-x-109">layer1</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">layer2</span><span
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class="cmmi-10x-x-109">> </span><span
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class="cmitt-10x-x-109">[</span><span
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class="cmmi-10x-x-109"><</span><span
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class="cmitt-10x-x-109">layer3</span><span
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class="cmmi-10x-x-109">></span><span
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class="cmitt-10x-x-109">...]</span>
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<!--l. 29--><p class="noindent" ><span
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class="cmbx-10x-x-109">DESCRIPTION</span>
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<!--l. 29--><p class="indent" > Compute and print on output the total degree <span
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class="cmmi-10x-x-109">o</span><sub><span
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class="cmmi-8">i</span></sub> of each node <span
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class="cmmi-10x-x-109">i </span>of a
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multiplex, defined as:
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<table
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class="equation-star"><tr><td>
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<center class="math-display" >
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<img
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src="mammult_doc0x.png" alt=" ∑ ∑ [α]
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oi = aij
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α j
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" class="math-display" ></center></td></tr></table>
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<!--l. 29--><p class="nopar" >
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<!--l. 29--><p class="noindent" >and the corresponding Z-score:
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<table
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class="equation-star"><tr><td>
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<center class="math-display" >
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<img
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src="mammult_doc1x.png" alt=" oi − ⟨o⟩
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z(oi) = ---σ---
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o
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" class="math-display" ></center></td></tr></table>
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<!--l. 29--><p class="nopar" >
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<!--l. 29--><p class="noindent" >where <span
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class="cmsy-10x-x-109">⟨</span><span
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class="cmmi-10x-x-109">o</span><span
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class="cmsy-10x-x-109">⟩ </span>and <span
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class="cmmi-10x-x-109">σ</span><sub><span
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class="cmmi-8">o</span></sub> are, respectively, the mean and the standard deviation of the
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total degree computed over all the active nodes of the multiplex.
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<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
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in the format:
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<!--l. 29--><p class="indent" >   <span
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class="cmti-10x-x-109">src</span><span
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class="cmti-10x-x-109">_ID dest</span><span
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class="cmti-10x-x-109">_ID</span>
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<!--l. 29--><p class="indent" > where <span
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class="cmti-10x-x-109">src</span><span
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class="cmti-10x-x-109">_ID </span>and <span
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class="cmti-10x-x-109">dest</span><span
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class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
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edge.
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<!--l. 43--><p class="noindent" ><span
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class="cmbx-10x-x-109">OUTPUT</span>
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<!--l. 43--><p class="indent" > The program prints on <span
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class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
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<!--l. 43--><p class="indent" >   <span
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class="cmti-10x-x-109">ID</span><span
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class="cmti-10x-x-109">_n deg</span><span
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class="cmti-10x-x-109">_n z</span><span
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class="cmti-10x-x-109">_n</span>
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<!--l. 43--><p class="indent" > where <span
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class="cmti-10x-x-109">ID</span><span
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class="cmti-10x-x-109">_n </span>is the ID of the node, <span
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class="cmti-10x-x-109">deg</span><span
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class="cmti-10x-x-109">_n </span>is its total degree, and <span
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class="cmti-10x-x-109">z</span><span
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class="cmti-10x-x-109">_n </span>is the
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corresponding Z-score.
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<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
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a node ID is not present in any of the layer files given as input, the program
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considers it as being isolated on all the layers, and the node is omitted from the
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output.
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<!--l. 45--><p class="noindent" ><span
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class="cmbx-10x-x-109">REFERENCE</span>
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<!--l. 45--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
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networks”, <span
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class="cmti-10x-x-109">Phys. Rev. E </span><span
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class="cmbx-10x-x-109">89</span>, 032804 (2014).
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<!--l. 45--><p class="indent" > Link to paper: <a
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href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
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class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
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