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authorKatolaZ <katolaz@yahoo.it>2015-10-19 16:30:12 +0100
committerKatolaZ <katolaz@yahoo.it>2015-10-19 16:30:12 +0100
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treeb6c0d31342f7af9d605ee83cfffe251554a307d4 /doc/latex/latex/structure/correlations/fit_knn.tex
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First commit of MAMMULT documentation
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+\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
+ }