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Netw Neurosci. 2017 Feb 1;1(1):31-41. doi: 10.1162/NETN_a_00004. eCollection 2017 Winter.

Nonrandom network connectivity comes in pairs.

Author information

Frankfurt Institute for Advanced Studies (FIAS), Johann Wolfgang Goethe University, Frankfurt am Main, Germany.
International Max Planck Research School for Neural Circuits, Max Planck Institute for Brain Research, Frankfurt am Main, Germany.


Overrepresentation of bidirectional connections in local cortical networks has been repeatedly reported and is a focus of the ongoing discussion of nonrandom connectivity. Here we show in a brief mathematical analysis that in a network in which connection probabilities are symmetric in pairs, Pij = Pji , the occurrences of bidirectional connections and nonrandom structures are inherently linked; an overabundance of reciprocally connected pairs emerges necessarily when some pairs of neurons are more likely to be connected than others. Our numerical results imply that such overrepresentation can also be sustained when connection probabilities are only approximately symmetric.


Bidirectional connections; Cortical circuit; Nonrandom connectivity; Random graph model

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

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