From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity

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.

Graph analysis of looming-selective networks in the tectum, and its replication in a simple computational model

“…Our definition of flow hierarchy was inspired by (Mones et al, 2012;Czégel and Palla, 2015), but based on modified (weighted) Katz centrality (Katz, 1953;Fletcher and Wennekers, 2018). To calculate Katz centrality, we assumed that each node j collected flows of incoming signals through all edges w ji leading to this node.…”

“…Flow hierarchy is a measure of structural hierarchy in the network (Mones et al, 2012), assessed through flows of activation that propagate through it. We based our measure of hierarchy on the distribution of Katz centrality values (Katz 1953;Fletcher and Wennekers 2018; see next section for definitions). Intuitively, hierarchy is high when a network has groups of "input" and "output" nodes, with connections between them largely pointing in the same direction, as it happens in layered feed-forward networks; hierarchy is weak in random networks, or networks that consist of cycles with no clear inputs and outputs (Czégel and Palla, 2015).…”

“…To identify information sinks, for each cell we calculated its Katz centrality within the graph (Katz, 1953;Fletcher and Wennekers, 2018). By definition, nodes with high Katz centrality have many paths leading to them, so a spike originating at random within a graph is more likely to eventually cause activation of these nodes, compared to nodes with low Katz centrality.…”

“…As cells with higher Katz centrality tend to be activated more often (Fletcher and Wennekers, 2018), we checked whether selectivity for looming stimuli correlated with cell average spiking activity in our recordings. We found that both in younger and older animals, actively spiking cells tended to have stronger looming selectivity (for stage 46 average r S = 0.34±0.20, r > 0 with p t1 = 2e-5; for stage 49 r S = 0.14±0.26, p t1 = 0.04, indicating a discernible decrease with development p t = 4e-4; across all cells r S = 0.07, p r = 4e-4).…”

Transport networks and towns in Roman and early medieval England: An application of PageRank to archaeological questions

“…The intended purpose of 48 such ranking was to filter the web pages and return the most relevant ones in response to a 49 query given to the search engine. However, the algorithm itself is universal and can usefully 50 be applied to other situations where one seeks to identify the importance of entities in a 51 networked system (for example, citation networks (Bollen et al, 2007;Ma et al, 2008), 52 biological networks (Banky et al, 2013;Fletcher and Wennekers, 2017; Ivan and Grolmusz, 53 2011), human movement (Gleich, 2015;Jiang et al, 2008), linguistics (Esuli and Sebastiani, 54 2007), or even networks of graduates' education institutes and employers (Schmidt and 55 Chingos, 2007)). Jiang (2009), in particular, has shown that there is a strong correlation 56 between the topological structure of human movement and PageRank scores in modern street 57 patterns.…”