  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.
