Network Communities of Dynamical Influence

Abstract

Fuelled by a desire for greater connectivity, networked systems now pervade our society at an unprecedented level that will affect it in ways we do not yet understand. In contrast, nature has already developed efficient networks that can instigate rapid response and consensus when key elements are stimulated. We present a technique for identifying these key elements by investigating the relationships between a system’s most dominant eigenvectors. This approach reveals the most effective vertices for leading a network to rapid consensus when stimulated, as well as the communities that form under their dynamical influence. In applying this technique, the effectiveness of starling flocks was found to be due, in part, to the low outdegree of every bird, where increasing the number of outgoing connections can produce a less responsive flock. A larger outdegree also affects the location of the birds with the most influence, where these influentially connected birds become more centrally located and in a poorer position to observe a predator and, hence, instigate an evasion manoeuvre. Finally, the technique was found to be effective in large voxel-wise brain connectomes where subjects can be identified from their influential communities.

Eigenvector alignment: Assessing functional network changes in amnestic mild cognitive impairment and Alzheimer’s disease

“…The theoretical basis for eigenvector alignment, proposed in this paper as a tool for detecting and quantifying changes in functional alignment, is a method of influential community detection, referred to as communities of dynamical influence (CDI) [ 12 ]. Communities are usually detected by an increased density of connections, but for CDI this density is implicitly captured by proximity and alignment to the network’s most influential nodes.…”

Mapping of shifting tidal estuaries to support inshore rescue

“…This grouping method has been detailed previously for network community detection using a Euclidean space defined by the network's dominant eigenvectors. 28 The pixels that are most prominent are far from the origin of this Euclidean space and have the largest scalar projection in the direction of their position vector when compared with all other pixels. To reduce computation only the top 50,000 pixels, which are furthest from the origin, are considered as potential group leaders.…”

Network Influence Based Classification and Comparison of Neurological Conditions

“…The network is assigned into Communities of Dynamical Influence (CDI) based on the connections and influence of nodes in the network. CDI are defined in [5] where community designation is achieved by using multiple (often three) eigenvectors to define a coordinate system. The nodes, which are further from the origin of this system than any of their connections, are defined as leaders of separate communities.…”

“…In this paper, CDI is determined from the three most dominant eigenvectors of the undirected connectivity matrix after applying the CST. These are the eigenvectors associated with the largest eigenvalues in magnitude and are shown in [5] to identify the nodes that are most effective at driving the network to consensus.…”

“…This influence is captured from resting state fMRI data that is converted into a network of brain regions, with connections weighted by the strength of their signal correlations [4]. A region's influence is determined using an eigenvector-based community detection, communities of dynamical influence (CDI), as introduced by Clark, Punzo and Macdonald (2019) [5]. For a directed graph, this influence represents the nodes that can rapidly lead the network to a new state of consensus.…”