![∑ ∑ ∑ [α]
∗ ∑--∑-i--j>i---αaij----
ω = i j>i(1− δ ∑ [α])
0, α aij](mammult_doc4x.png)
NAME
avg_edge_overlap.py - compute the average edge overlap of a multiplex.
SYNOPSYS
avg_edge_overlap.py <layer1> [<layer2>...]
DESCRIPTION
Compute and print on output the average edge overlap
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i.e., the expected number of layers on which an edge of the multiplex exists, and the corresponding normalised quantity:
![∑ ∑ ∑ a[α]
ω = ---∑--∑i--j>i--α--ij-----
M i j>i(1− δ0,∑α a[iαj] )](mammult_doc5x.png) |
that is the expected fraction of layers on which an edge of the multiplex is present.
Each input file contains the (undirected) edge list of a layer, and each line is in the format:
src_ID dest_ID
where src_ID and dest_ID are the IDs of the two endpoints of an edge.
OUTPUT
The program prints on stdout a single line, in the format:
omega_star omega
where omega_star and omega are, respectively, the expected number and fraction of layers in which an edge is present.
REFERENCE
F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex networks”, Phys. Rev. E 89, 032804 (2014).
Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804
L. Lacasa, V. Nicosia, V. Latora, “Network structure of multivariate time series”, accepted for publication in Scientific Reports, arxiv:1408.0925 (2015).
Link to paper: http://arxiv.org/abs/1408.0925