Abstract
We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman–Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman–Ricci curvature with another well-known notion of network curvature, namely the Ollivier–Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of adhd patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.
Highlights
It is a common research practice to study the properties of complex interconnected systems by representing them as heterogeneous networks and using various network-theoretic tools for their analysis[1,2]
We provide a formal definition of the network anomaly detection problem following a mathematical framework similar to what is described in[12]
To identify critical components of a temporal network, one first needs to provide details for the following four specific items: (i) the network model under consideration, (ii) a definition of the elementary components of the network, and (iii) how the network changes over time, (iv) the property of the network that will be used to identify critical components
Summary
It is a common research practice to study the properties of complex interconnected systems by representing them as heterogeneous networks and using various network-theoretic tools for their analysis[1,2] Such heterogeneous networks may vary in diversity from simple undirected networks to edge-labeled directed networks. Examples of such networks include biological signal transduction networks with node dynamics, biochemical reaction networks, infectious disease contact networks, and time-evolving correlation n etworks[3] Such networks may have a set of critical elementary components (or “critical” components) whose presence or absence alters a significant global property of these networks between two time steps.
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