E-mail network at Universitat Rovira i Virgili
Self-similarity in the community structure
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(a) Calculation of the community
size distribution for a binary tree generated by the community identification
algorithm. Black nodes represent the actual nodes of the original graph while
white nodes are just graphical representations of communities that arise as a
result of the splitting procedure. Nodes A and B belong to a community of
size 2, and together with E form a community of size 3. Similarly, C, D and F
form another community of size 3. These two groups together form a higher
level community of size 6. Following up to higher and higher levels, the
community structure can be regarded as the set of nested groups. In this case
there are three communities of size 2, three communities of size 3, one
community of size 6, one community of size 7, and one community of size 10.
Note that a single node belongs to different communities at different levels.
(b) Calculation of the drainage area distribution for a river network. (c)
Calculation of the Horton-Strahler index. In this case, there are 10 branches
with index 1, 3 branches with index 2, and 1 branch with index 3. (d) The
distribution of community sizes, P(s). The distribution of community sizes in
a random network is shown with a dotted line for comparison. (e) The number
of branches with HS index i, as a function of i. The community tree of the
e-mail network is topologically self-similar with B=5.76. Topological
self-similarity does not hold for the random case. |
Albert Díaz-Guilera