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+\myprogram{{knn\_q\_from\_degrees.py}}
+ {compute the inter-layer degree-degree correlation function.}
+ {$<$filein$>$}
+
+\mydescription{Compute the inter-layer degree
+ correlation functions for two layers of a multiplex, using
+ the degrees of the nodes specified in the input file. The
+ format of the input file is as follows
+
+\hspace{0.5cm} \textit{ki qi}
+
+where \textit{ki} and \textit{qi} are, respectively, the degree at
+layer 1 and the degree at layer 2 of node \textit{i}.
+
+ If we consider two layers of a multiplex, and we denote by
+ $k$ the degree of a node on the first layer and by $q$ the
+ degree of the same node on the second layers, the
+ inter-layer degree correlation function is defined as
+
+ \begin{equation*}
+ \overline{k}(q) = \frac{1}{N_{k}}\sum_{k'} k' P(k'|q)
+ \end{equation*}
+
+ where $P(k'|q)$ is the probability that a node with degree
+ $q$ on the second layer has degree equal to $k'$ on the
+ first layer, and $N_k$ is the number of nodes with degree
+ $k$ on the first layer. The quantity $\overline{k}(q)$ is
+ the expected degree at layer $1$ of node that have degree
+ equal to $q$ on layer $2$. The dual quantity:
+
+ \begin{equation*}
+ \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k)
+ \end{equation*}
+
+ is the average degree on layer $2$ of nodes having degree
+ $k$ on layer $1$.
+}
+
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in
+ the format:
+
+ \hspace{0.5cm} \textit{k $\overline{q}(k)$}
+
+ where \textit{k} is the degree on layer $1$ and
+ $\overline{q}(k)$ is the average degree on layer $2$ of
+ nodes having degree equal to $k$ on layer $1$.
+
+ The program also prints on \texttt{stderr} a list of lines in
+ the format:
+
+ \hspace{0.5cm} \textit{q $\overline{k}(q)$}
+
+ where \textit{q} is the degree on layer $2$ and
+ $\overline{k}(q)$ is the average degree on layer $1$ of
+ nodes having degree equal to $q$ on layer $2$.
+ }
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }