\myprogram{{fit\_knn}}
          {power-law fit of the inter-layer degree correlation
          function.}  
          {$<$filein$>$ $<$alpha$>$}

\mydescription{Perform a power-law fit of the inter-layer degree
          correlation function:

          \begin{equation*}
           \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k)
          \end{equation*}

          where $k$ is the degree of a node on layer $1$, $q$ is the
          degree on layer $2$ and $P(q|k)$ is the probability that a
          node with degree $k$ on layer $1$ has degree $q$ on layer
          $2$. The program assumes that $\overline{q}(k)$ can be
          written in the form $a k^{b}$, and computes the two
          parameters $a$ and $b$ through a linear fit of the log-log
          plot of $\overline{q}(k)$.

          The input file \textit{filein} contains a list of lines in
          the format:

          \hspace{0.5cm} \textit{ki qi}

          where \textit{ki} is the degree of node $i$ at layer $1$
          and \textit{qi} is the degree of node $i$ at layer $2$. 

          The second parameter \textit{alpha} is the ratio of the
          progression used to generate the exponentially-distributed
          bins for the log-log plot. Typical values of \textit{alpha}
          are between $1.1$ and $2.0$.
          
          
          N.B.: The exponent $b$ computed with this method is known to
          be inaccurate.
}



\myreturn{The program prints on \texttt{stdout} the values of the
          parameters $a$ and $b$ of the power-law fit $\overline{q}(k)
          = a k^{b}$.}

\myreference{\refcorrelations

  \refgrowth

  \refnonlinear
  }
