Milos Kudelka, Eliska Ochodkova, Sarka Zehnalova, Jakub Plesnik
SpringerOpen : Applied Network Science : Community structure in networks
VSB - Technical University of Ostrava, CS Dept.
17. listopadu 2172/15, 708 00
Czech Republic
Supplement
Example: Zachary's karate club
This example shows automatically detected prominent nodes and ego-zones in the network.
The algorithm published in the article above is based on the analysis of non-symmetric relationships between nodes.
Fig. 1: Three types on network nodes
Strongly (red), weakly (yellow), and non (green) prominent nodes are detected in the network.
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Arrows represent non-symmetric structural dependencies between nodes.
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Mutually dependent/independent nodes have a strong/weak relationship.
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We published more about the non-symmetric structural dependency in
Local Dependency in Networks
Fig. 2: Ego-zones generated by prominent egos
Overlapping and nested zones are detected around strongly, and weakly prominent nodes (red egos except node 31).
- One zone may have multiple egos; in this case, these egos generate the same zones.
- Dark blue nodes are zone liaisons; light blue nodes are zone co-liaisons; yellow nodes are other members of zones.
- Zones generated by egos 1, 34, 3, and 32 are not nested in another zone; all of these egos are strongly prominent nodes.
Fig 3: Ego-zones generated by non-prominent egos
A selection of additional zones; a total of 29 zones are detected in Zachary's karate club.
- These and other zones consist only of non-prominent egos, liaisons, and co-liaisons (including the zone above generated by node 31).
- All these zones are nested at least in one another zone.
- The remaining zones are [12 1] [13 1-4] [15 33-34] [16 33-34] [18 1-2] [19 33-34] [20 1-2] [21 33-34] [22 1-2] [23 33-34] [27 30-34] [28] [29 32-34].
- Node 28 is not a member of any non-trivial zone because it is mutually independent with all its neighbors.
Milos Kudelka, 2020, milos.kudelka@vsb.cz