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<head><title>1.1.3.0 overlap_degree.py</title> 
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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">&#x003C;</span><span 
class="cmitt-10x-x-109">layer1</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">layer2</span><span 
class="cmmi-10x-x-109">&#x003E; </span><span 
class="cmitt-10x-x-109">[</span><span 
class="cmmi-10x-x-109">&#x003C;</span><span 
class="cmitt-10x-x-109">layer3</span><span 
class="cmmi-10x-x-109">&#x003E;</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="    &sum;   &sum;   [&alpha;]
oi =       aij
     &alpha;   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 &minus; &#x27E8;o&#x27E9;
z(oi) = ---&sigma;---
           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">&#x27E8;</span><span 
class="cmmi-10x-x-109">o</span><span 
class="cmsy-10x-x-109">&#x27E9; </span>and <span 
class="cmmi-10x-x-109">&sigma;</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" >   &#x00A0;    <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" >   &#x00A0;     <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, &#8220;Structural measures for multiplex
networks&#8221;, <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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