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+\myprogram{{cartography\_from\_layers.py}}
+ {compute the total degree and the multiplex participation
+ coefficient of all the nodes of a multiplex.} {$<$layer1$>$
+ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the total degree and the multiplex participation
+ coefficient $P_i$ for each node $i$ of a multiplex. The
+ participation coefficient is defined as:
+
+ \begin{equation*}
+ P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right]
+ \end{equation*}
+
+ \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$
+ if and only if node $i$ is active on exactly one of the layers,
+ while $P_i=1$ if node $i$ has equal degree on all the $M$ layers.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{deg\_n P\_n col\_n}
+
+ where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n}
+ is the participation coefficient of node $n$ and \textit{col} is the
+ integer representation of the activity bitstring of node $n$, which
+ is a number between $0$ and $2^{M}-1$. The field \textit{col} 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.
+
+ \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.
+ }
+
+\myreference{\refmetrics}