diff options
Diffstat (limited to 'doc/latex/latex/structure/metrics/part_coeff.tex')
-rw-r--r-- | doc/latex/latex/structure/metrics/part_coeff.tex | 43 |
1 files changed, 43 insertions, 0 deletions
diff --git a/doc/latex/latex/structure/metrics/part_coeff.tex b/doc/latex/latex/structure/metrics/part_coeff.tex new file mode 100644 index 0000000..f3afd7d --- /dev/null +++ b/doc/latex/latex/structure/metrics/part_coeff.tex @@ -0,0 +1,43 @@ +\myprogram{{part\_coeff.py}} + {compute the multiplex partifipation coefficient of all the nodes of + a multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the multiplex participation + coefficient $P_i$ for each node $i$ of a multiplex. The + participation coefficient is defined as: + + \begin{equation*} + P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right] + \end{equation*} + + \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$ + if and only if node $i$ is active on exactly one of the layers, + while $P_i=1$ if node $i$ has equal degree on all the $M$ layers. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{deg\_n P\_n col\_n} + + where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n} + is the participation coefficient of node $n$ and \textit{col} is the + integer representation of the activity bitstring of node $n$, which + is a number between $0$ and $2^{M}-1$. The field \textit{col} might + be useful in visualisations, where it would be possible to associate + different colors to nodes having diffrent node activity patterns. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers, and is set to zero. + } + +\myreference{\refmetrics} |