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diff --git a/doc/latex/latex/structure/correlations/fit_knn.tex b/doc/latex/latex/structure/correlations/fit_knn.tex new file mode 100644 index 0000000..cb90c2b --- /dev/null +++ b/doc/latex/latex/structure/correlations/fit_knn.tex @@ -0,0 +1,50 @@ +\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 + } |