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<head><title>1.1.4.0 avg_edge_overlap.py</title>
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<h5 class="subsubsectionHead"><a
id="x25-240001.1.4"></a><span
class="cmtt-10x-x-109">avg</span><span
class="cmtt-10x-x-109">_edge</span><span
class="cmtt-10x-x-109">_overlap.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">avg</span><span
class="cmbx-10x-x-109">_edge</span><span
class="cmbx-10x-x-109">_overlap.py </span>- compute the average edge overlap of a multiplex.
<!--l. 3--><p class="noindent" ><span
class="cmbx-10x-x-109">SYNOPSYS</span>
<!--l. 3--><p class="indent" > <span
class="cmbx-10x-x-109">avg</span><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. 29--><p class="noindent" ><span
class="cmbx-10x-x-109">DESCRIPTION</span>
<!--l. 29--><p class="indent" > Compute and print on output the average edge overlap
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc4x.png" alt=" ∑ ∑ ∑ [α]
∗ ∑--∑-i--j>i---αaij----
ω = i j>i(1− δ ∑ [α])
0, α aij
" class="math-display" ></center></td></tr></table>
<!--l. 29--><p class="nopar" >
<!--l. 29--><p class="noindent" >i.e., the expected <span
class="cmti-10x-x-109">number </span>of layers on which an edge of the multiplex exists, and
the corresponding normalised quantity:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc5x.png" alt=" ∑ ∑ ∑ a[α]
ω = ---∑--∑i--j>i--α--ij-----
M i j>i(1− δ0,∑α a[iαj] )
" class="math-display" ></center></td></tr></table>
<!--l. 29--><p class="nopar" >
<!--l. 29--><p class="noindent" >that is the expected <span
class="cmti-10x-x-109">fraction </span>of layers on which an edge of the multiplex is
present.
<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
in the format:
<!--l. 29--><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. 29--><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. 38--><p class="noindent" ><span
class="cmbx-10x-x-109">OUTPUT</span>
<!--l. 38--><p class="indent" > The program prints on <span
class="cmtt-10x-x-109">stdout </span>a single line, in the format:
<!--l. 38--><p class="indent" >   <span
class="cmti-10x-x-109">omega</span><span
class="cmti-10x-x-109">_star omega</span>
<!--l. 38--><p class="noindent" >where <span
class="cmti-10x-x-109">omega</span><span
class="cmti-10x-x-109">_star </span>and <span
class="cmti-10x-x-109">omega </span>are, respectively, the expected number and fraction
of layers in which an edge is present.
<!--l. 42--><p class="noindent" ><span
class="cmbx-10x-x-109">REFERENCE</span>
<!--l. 42--><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. 42--><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>
<!--l. 42--><p class="indent" > L. Lacasa, V. Nicosia, V. Latora, <span
class="cmti-10x-x-109">“Network structure of multivariate time</span>
<span
class="cmti-10x-x-109">series”</span>, accepted for publication in Scientific Reports, arxiv:1408.0925
(2015).
<!--l. 42--><p class="indent" > Link to paper: <a
href="http://arxiv.org/abs/1408.0925" class="url" ><span
class="cmtt-10x-x-109">http://arxiv.org/abs/1408.0925</span></a>
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