Overrepresentation of bidirectional connections in local cortical networks has been repeatedly reported and is in the focus of the ongoing discussion of non-random connectivity. Here we show in a brief mathematical analysis that in a network in which connection probabilities are symmetric in pairs, Pij=Pji, the occurrence of bidirectional connections and non-random structures are inherently linked; an overabundance of reciprocally connected pairs emerges necessarily when the network structure deviates from a random network in any form.
Cite
@article{arxiv.1609.04245,
title = {Non-random network connectivity comes in pairs},
author = {Felix Z. Hoffmann and Jochen Triesch},
journal= {arXiv preprint arXiv:1609.04245},
year = {2016}
}