Abstract
It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory-inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to hold. We argue that the reason Katz centrality correlates so highly with neuronal activity compared to other centrality measures is because it nicely captures disinhibition in neural networks. In addition, we argue that these theoretical findings are applicable to neuroscientists who apply centrality measures to functional brain networks, as well as offer a neurophysiological justification to high level cognitive models which use certain centrality measures.
Highlights
Understanding large complex networks has become increasingly important due to an increase of networked data
It is known that PageRank, as well as other centrality measures using the power method such as Hyperlink-Induced Topic Search (HITS), is not guaranteed to converge when there are negative weights,[17] this is why NA is often reported for PageRank
We argued that if a neural network is in a resting state and the neurons have a wide range of activation the Katz centrality of a neuron correlates exceedingly well with its relative firing rate
Summary
Understanding large complex networks has become increasingly important due to an increase of networked data. It seems crucially related to the generation of epileptiform brain activity.[43,49,61] Small-world properties of cortical connectivity have further been related to general intelligence and creativity.[33,39,51] Graph Index Complexity, which measures the heterogeneity of edges in a network, is found to be lower in patients with mild cognitive impairment.[1] Visibility graph analysis has proved successful for processing EEG data with the goal of identifying patients with Alzheimer’s Disease, ADHD and Autism.[2,3,4] The reader is referred to Ref. 14 which gives a good overview of network theory in general applied to structural and functional networks in the brain. The particular property of networks and their relation to cortical networks this paper is concerned with, is the concept of centrality
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