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author | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
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committer | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
commit | a86962cbfd0321387c920a04188512d0de2f3036 (patch) | |
tree | b6c0d31342f7af9d605ee83cfffe251554a307d4 /doc/latex/latex/structure/metrics/edge_overlap.tex | |
parent | df8386f75b0538075d72d52693836bb8878f505b (diff) |
First commit of MAMMULT documentation
Diffstat (limited to 'doc/latex/latex/structure/metrics/edge_overlap.tex')
-rw-r--r-- | doc/latex/latex/structure/metrics/edge_overlap.tex | 36 |
1 files changed, 36 insertions, 0 deletions
diff --git a/doc/latex/latex/structure/metrics/edge_overlap.tex b/doc/latex/latex/structure/metrics/edge_overlap.tex new file mode 100644 index 0000000..64d7dbf --- /dev/null +++ b/doc/latex/latex/structure/metrics/edge_overlap.tex @@ -0,0 +1,36 @@ +\myprogram{{edge\_overlap.py}} + {compute the edge overlap of all the edges of the + multiplex.} + {$<$layer1$>$ [$<$layer2$>$...]} + +\mydescription{Compute and print on output the edge overlap $o_{ij}$ of each + edge of the multiplex. Given a pair of nodes $(i,j)$ that + are directly connected on at least one of the $M$ layers, + the edge overlap $o_{ij}$ is defined as: + + \begin{equation*} + o_{ij} = \sum_{\alpha}a_{ij}\lay{\alpha} + \end{equation*} + + \noindent i.e., the number of layers on which the edge $(i,j)$ + exists. + + + 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{ID\_1 ID\_2 overlap} + + \noindent where \textit{ID\_1} and \textit{ID\_2} are the IDs of the + end-points of the edge, and \textit{overlap} is the number of layers + in which the edge exists.} + +\myreference{\refmetrics} |