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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}
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