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+\myprogram{{avg\_edge\_overlap.py}}
+ {compute the average edge overlap of a multiplex.}
+ {$<$layer1$>$ [$<$layer2$>$...]}
+
+\mydescription{Compute and print on output the average edge overlap
+
+ \begin{equation*} \omega^{*}
+ = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{ \sum_{i}\sum_{j>i}(1
+ - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})} \end{equation*}
+
+ \noindent i.e., the expected \textit{number} of layers on which an
+ edge of the multiplex exists, and the corresponding normalised
+ quantity:
+
+ \begin{equation*}
+ \omega = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{M \sum_{i}\sum_{j>i}(1
+ - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})}
+ \end{equation*}
+
+ \noindent that is the expected \textit{fraction} of layers on which
+ an edge of the multiplex is present.
+
+ 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 single line, in the
+ format:
+
+ \hspace{0.5cm} \textit{omega\_star omega}
+
+ \noindent where \textit{omega\_star} and \textit{omega} are,
+ respectively, the expected number and fraction of layers in which an
+ edge is present.}
+
+\myreference{\refmetrics
+
+ \vspace{0.5cm}\refvisibility}