Download Statistical models of network connectivity in cortical microcircuits

Statistical models of network connectivity in cortical microcircuits
Marina Vegué and Alex Roxin, CRM
Network topology determines the ability of neural networks to store and
transmit information. In network models the topology is usually represented by
a directed graph, which is a set of nodes (the neurons) and a set of directed
edges that connect them in a precise manner. One of the challenges of network
modeling is, therefore, the construction of random graphs that reflect both the
variability and the main structural properties of real neural networks.
Erdös-Rényi (ER) graphs, defined by a single parameter p which determines the
probability of any directed edge, are among the simplest random models. Some
experimental studies suggest, however, that cortical microcircuits are not well
represented by ER models [1,2]. One major finding that supports this idea is
the fact that the probability of a directed connection between a pair of neurons
increases with the number of common neighbors they have [2].
In this work we have studied several random models and tried to determine to
what extent they reproduce this “common neighbor rule”. Our results indicate
that the fact that nodes tend to be more connected as they share more neighbors
is a general property that emerges from very different models. We have focused
on the “configuration model”, which is defined by setting the distribution for
the in- and out-degrees of the network. In this model, the common neighbor
rule can be easily understood in terms of the expectation of the in- and outdegree of a node conditioned to the number of common neighbors it shares
with another node. These results suggest that, rather than being a fingerprint of
a particular topology, the common neighbor rule is a universal property of many
random networks.
[1] Song et al. PLoS Biol. 3(3) (2005)
[2] Perin et al. PNAS 108(13) (2011)