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<head><title>1.1.4.0 edge_overlap.py</title>
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<h5 class="subsubsectionHead"><a
id="x23-220001.1.4"></a><span
class="cmtt-10x-x-109">edge</span><span
class="cmtt-10x-x-109">_overlap.py</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">edge</span><span
class="cmbx-10x-x-109">_overlap.py </span>- compute the edge overlap of all the edges of the
multiplex.
<!--l. 4--><p class="noindent" ><span
class="cmbx-10x-x-109">SYNOPSYS</span>
<!--l. 4--><p class="indent" > <span
class="cmbx-10x-x-109">edge</span><span
class="cmbx-10x-x-109">_overlap.py </span><span
class="cmmi-10x-x-109"><</span><span
class="cmitt-10x-x-109">layer1</span><span
class="cmmi-10x-x-109">> </span><span
class="cmitt-10x-x-109">[</span><span
class="cmmi-10x-x-109"><</span><span
class="cmitt-10x-x-109">layer2</span><span
class="cmmi-10x-x-109">></span><span
class="cmitt-10x-x-109">...]</span>
<!--l. 25--><p class="noindent" ><span
class="cmbx-10x-x-109">DESCRIPTION</span>
<!--l. 25--><p class="indent" > Compute and print on output the edge overlap <span
class="cmmi-10x-x-109">o</span><sub><span
class="cmmi-8">ij</span></sub> of each edge of the
multiplex. Given a pair of nodes (<span
class="cmmi-10x-x-109">i,j</span>) that are directly connected on at least one
of the <span
class="cmmi-10x-x-109">M </span>layers, the edge overlap <span
class="cmmi-10x-x-109">o</span><sub><span
class="cmmi-8">ij</span></sub> is defined as:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc3x.png" alt=" ∑ [α]
oij = aij
α
" class="math-display" ></center></td></tr></table>
<!--l. 25--><p class="nopar" >
<!--l. 25--><p class="noindent" >i.e., the number of layers on which the edge (<span
class="cmmi-10x-x-109">i,j</span>) exists.
<!--l. 25--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
in the format:
<!--l. 25--><p class="indent" >   <span
class="cmti-10x-x-109">src</span><span
class="cmti-10x-x-109">_ID dest</span><span
class="cmti-10x-x-109">_ID</span>
<!--l. 25--><p class="indent" > where <span
class="cmti-10x-x-109">src</span><span
class="cmti-10x-x-109">_ID </span>and <span
class="cmti-10x-x-109">dest</span><span
class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
edge.
<!--l. 34--><p class="noindent" ><span
class="cmbx-10x-x-109">OUTPUT</span>
<!--l. 34--><p class="indent" > The program prints on <span
class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
<!--l. 34--><p class="indent" >   <span
class="cmti-10x-x-109">ID</span><span
class="cmti-10x-x-109">_1 ID</span><span
class="cmti-10x-x-109">_2 overlap</span>
<!--l. 34--><p class="noindent" >where <span
class="cmti-10x-x-109">ID</span><span
class="cmti-10x-x-109">_1 </span>and <span
class="cmti-10x-x-109">ID</span><span
class="cmti-10x-x-109">_2 </span>are the IDs of the end-points of the edge, and <span
class="cmti-10x-x-109">overlap </span>is
the number of layers in which the edge exists.
<!--l. 36--><p class="noindent" ><span
class="cmbx-10x-x-109">REFERENCE</span>
<!--l. 36--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
networks”, <span
class="cmti-10x-x-109">Phys. Rev. E </span><span
class="cmbx-10x-x-109">89</span>, 032804 (2014).
<!--l. 36--><p class="indent" > Link to paper: <a
href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
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