blob: cb90c2b0cc4bdcb37572e45bb93966b7aec53594 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
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
}
|
