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<h5 class="subsubsectionHead"><a
id="x19-180001.1.3"></a><span
class="cmtt-10x-x-109">overlap</span><span
class="cmtt-10x-x-109">_degree.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">overlap</span><span
class="cmbx-10x-x-109">_degree.py </span>- compute the total (overlapping) degree of all the nodes
of a multiplex and the corresponding Z-score.
<!--l. 3--><p class="noindent" ><span
class="cmbx-10x-x-109">SYNOPSYS</span>
<!--l. 3--><p class="indent" > <span
class="cmbx-10x-x-109">overlap</span><span
class="cmbx-10x-x-109">_degree.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">layer2</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">layer3</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 total degree <span
class="cmmi-10x-x-109">o</span><sub><span
class="cmmi-8">i</span></sub> of each node <span
class="cmmi-10x-x-109">i </span>of a
multiplex, defined as:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc0x.png" alt=" ∑ ∑ [α]
oi = aij
α j
" class="math-display" ></center></td></tr></table>
<!--l. 29--><p class="nopar" >
<!--l. 29--><p class="noindent" >and the corresponding Z-score:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc1x.png" alt=" oi − ⟨o⟩
z(oi) = ---σ---
o
" class="math-display" ></center></td></tr></table>
<!--l. 29--><p class="nopar" >
<!--l. 29--><p class="noindent" >where <span
class="cmsy-10x-x-109">⟨</span><span
class="cmmi-10x-x-109">o</span><span
class="cmsy-10x-x-109">⟩ </span>and <span
class="cmmi-10x-x-109">σ</span><sub><span
class="cmmi-8">o</span></sub> are, respectively, the mean and the standard deviation of the
total degree computed over all the active nodes of the multiplex.
<!--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. 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>a list of lines in the format:
<!--l. 43--><p class="indent" >   <span
class="cmti-10x-x-109">ID</span><span
class="cmti-10x-x-109">_n deg</span><span
class="cmti-10x-x-109">_n z</span><span
class="cmti-10x-x-109">_n</span>
<!--l. 43--><p class="indent" > where <span
class="cmti-10x-x-109">ID</span><span
class="cmti-10x-x-109">_n </span>is the ID of the node, <span
class="cmti-10x-x-109">deg</span><span
class="cmti-10x-x-109">_n </span>is its total degree, and <span
class="cmti-10x-x-109">z</span><span
class="cmti-10x-x-109">_n </span>is the
corresponding Z-score.
<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
a node ID is not present in any of the layer files given as input, the program
considers it as being isolated on all the layers, and the node is omitted from the
output.
<!--l. 45--><p class="noindent" ><span
class="cmbx-10x-x-109">REFERENCE</span>
<!--l. 45--><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. 45--><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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