Article
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Filtering Statistics on Networks
Version 1
: Received: 31 July 2020 / Approved: 2 August 2020 / Online: 2 August 2020 (16:44:25 CEST)
A peer-reviewed article of this Preprint also exists.
Baxter, G.J.; da Costa, R.A.; Dorogovtsev, S.N.; Mendes, J.F.F. Filtering Statistics on Networks. Entropy 2020, 22, 1149. Baxter, G.J.; da Costa, R.A.; Dorogovtsev, S.N.; Mendes, J.F.F. Filtering Statistics on Networks. Entropy 2020, 22, 1149.
Abstract
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph’s degree.
Keywords
filtering; information; degeneracy; entropy; relevance; resolution; complexity; complex networks
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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