Non-random network connectivity comes in pairs

TL;DR

This paper demonstrates mathematically that non-random, symmetric pairwise connection probabilities in neural networks inherently lead to an overrepresentation of bidirectional connections, linking network structure deviations to reciprocal connection abundance.

Contribution

It provides a mathematical proof that symmetric pairwise connection probabilities naturally result in bidirectional connection overrepresentation in non-random networks.

Findings

Overrepresentation of bidirectional connections is mathematically linked to symmetric pairwise probabilities.

Non-random network structures inherently produce more reciprocal connections.

Symmetry in connection probabilities implies non-random connectivity features.

Abstract

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, $P_{ij} = P_{ji}$, 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.