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, P ij = P ji , 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. Abstract AUTHOR SUMMARY Understanding the specific connectivity of neural circuits is an important challenge of modern neuroscience. In this study we address an important feature of neural connectivity, the abundance of bidirectionally connected neuron pairs, which far exceeds what would be expected in a random network. Our theoretical analysis reveals a simple condition under which such an overrepresentation of bidirectionally connected pairs necessarily occurs: Any network in which both directions of connection are equally likely to exist in any given pair of neurons, but in which some pairs are more likely to be connected than others, must exhibit an abundance of reciprocal connections. This insight should guide the analysis and interpretation of future connectomics datasets.