Network bipartitioning in the anti-communicability Euclidean space
We define the anti-communicability function for the nodes of a simple graph as the nondiagonal entries of exp (-A). We prove that it induces an embedding of the nodes into a Euclidean space. The anti-communicability angle is then defined as the angle spanned by the position vectors of the correspond...
| Published in: | AIMS Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-11-01
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| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2021070/fulltext.html |
| Summary: | We define the anti-communicability function for the nodes of a simple graph as the nondiagonal entries of exp (-A). We prove that it induces an embedding of the nodes into a Euclidean space. The anti-communicability angle is then defined as the angle spanned by the position vectors of the corresponding nodes in the anti-communicability Euclidean space. We prove analytically that in a given k-partite graph, the anti-communicability angle is larger than 90° for every pair of nodes in different partitions and smaller than 90° for those in the same partition. This angle is then used as a similarity metric to detect the “best” k-partitions in networks where certain level of edge frustration exists. We apply this method to detect the “best” k-partitions in 15 real-world networks, finding partitions with a very low level of “edge frustration”. Most of these partitions correspond to bipartitions but tri- and pentapartite structures of real-world networks are also reported. |
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| ISSN: | 2473-6988 |