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<h5 class="subsubsectionHead"><a
id="x19-180001.1.3"></a><span
class="cmtt-10x-x-109">cartography</span><span
class="cmtt-10x-x-109">_from</span><span
class="cmtt-10x-x-109">_layers.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">cartography</span><span
class="cmbx-10x-x-109">_from</span><span
class="cmbx-10x-x-109">_layers.py </span>- compute the total degree and the multiplex
participation coefficient of all the nodes of a 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">cartography</span><span
class="cmbx-10x-x-109">_from</span><span
class="cmbx-10x-x-109">_layers.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. 24--><p class="noindent" ><span
class="cmbx-10x-x-109">DESCRIPTION</span>
<!--l. 24--><p class="indent" > Compute and print on output the total degree and the multiplex
participation coefficient <span
class="cmmi-10x-x-109">P</span><sub><span
class="cmmi-8">i</span></sub> for each node <span
class="cmmi-10x-x-109">i </span>of a multiplex. The participation
coefficient is defined as:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc2x.png" alt=" [ M [α] ]
-M---- ∑ ki--2
Pi = M − 1 1 − ( oi )
α=1
" class="math-display" ></center></td></tr></table>
<!--l. 24--><p class="nopar" >
<!--l. 24--><p class="noindent" >Note that <span
class="cmmi-10x-x-109">P</span><sub><span
class="cmmi-8">i</span></sub> takes values in [0<span
class="cmmi-10x-x-109">,</span>1], where <span
class="cmmi-10x-x-109">P</span><sub><span
class="cmmi-8">i</span></sub> = 0 if and only if node <span
class="cmmi-10x-x-109">i </span>is active on
exactly one of the layers, while <span
class="cmmi-10x-x-109">P</span><sub><span
class="cmmi-8">i</span></sub> = 1 if node <span
class="cmmi-10x-x-109">i </span>has equal degree on all the <span
class="cmmi-10x-x-109">M</span>
layers.
<!--l. 24--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
in the format:
<!--l. 24--><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. 24--><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">deg</span><span
class="cmti-10x-x-109">_n P</span><span
class="cmti-10x-x-109">_n col</span><span
class="cmti-10x-x-109">_n</span>
<!--l. 43--><p class="indent" > where <span
class="cmti-10x-x-109">deg</span><span
class="cmti-10x-x-109">_n </span>is the total degree of node <span
class="cmmi-10x-x-109">n</span>, <span
class="cmti-10x-x-109">P</span><span
class="cmti-10x-x-109">_n </span>is the participation coefficient
of node <span
class="cmmi-10x-x-109">n </span>and <span
class="cmti-10x-x-109">col </span>is the integer representation of the activity bitstring of node <span
class="cmmi-10x-x-109">n</span>,
which is a number between 0 and 2<sup><span
class="cmmi-8">M</span></sup> <span
class="cmsy-10x-x-109">− </span>1. The field <span
class="cmti-10x-x-109">col </span>might be useful for the
visualisation of the multiplex cartography diagram, where it would be
possible to associate different colors to nodes having different node activity
patterns.
<!--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 is set to
zero.
<!--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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