Mathematics, Department of


Date of this Version



Curto et al.: Pairwise correlation graphs from hippocampal population activity have highly non-random, low-dimensional clique topology. BMC Neuroscience 2013 14(Suppl 1): P182; doi:10.1186/1471-2202-14-S1-P182


Copyright 2013 Curto et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyzed the structure of cliques in pairwise correlation graphs obtained from population activity in hippocampus under a variety of behavioral conditions: open field exploration, wheel running, and sleep. Using topological data analysis, we found these graphs to be highly non-random by comparing their clique structure to that of Erdös-Rényi random graphs with matching edge probabilities. The clique topology in all three conditions was low-dimensional and consistent with what is theoretically expected from place cells during spatial navigation. Remarkably, the same pattern was also observed in the sleep data. To better understand how this correlation structure might arise, we considered a recurrent network with a simple Hebbian learning rule. We found the same clique structure emerged in the network when recurrent connections were formed in the presence of random sparse patterns of activity. This may provide a generic mechanism explaining how low-dimensional clique topology arises in hippocampal data.

Pairwise correlations are an important tool for understanding neuronal population activity [1]. Pairwise correlation graphs, where the edges reflect high levels of correlation between neurons, are often used as a proxy for underlying network connectivity. In this work, we are motivated by the question: What is the structure of pairwise correlations in hippocampal population activity? To address this question, we analyzed graded families of pairwise correlation graphs, parametrized by the threshold on correlation strength used to define the edges. In brain areas with receptive fields or place fields, the structure of the neural code has strong implications for structure of cliques in these graphs. This can be detected by examining the clique topology of the graph (specifically, topological invariants called ‘Betti numbers’ of the clique complex), and is closely tied to the dimension and topology of the underlying space [2]. For example, for hippocampal place cell activity during spatial exploration, pairwise correlation graphs are expected to have highly non-random and lowdimensional clique topology, due to the arrangement of place fields in a low-dimensional environment.