A straightforward edge centrality concept derived from generalizing degree and strength

Abstract

Vertex degree—the number of edges that are incident to a vertex—is a fundamental concept in network theory. It is the historically first and conceptually simplest centrality concept to rate the importance of a vertex for a network’s structure and dynamics. Unlike many other centrality concepts, for which joint metrics have been proposed for both vertices and edges, by now there is no concept for an edge centrality analogous to vertex degree. Here, we propose such a concept—termed nearest-neighbor edge centrality—and demonstrate its suitability for a non-redundant identification of central edges in paradigmatic network models as well as in real-world networks from various scientific domains.

Stimulation-related modifications of evolving functional brain networks in unresponsive wakefulness

“…Future work may also focus on other, e.g. more local network characteristics and address questions of whether network characteristics provide information for the selection and control of individual therapies 32 , 33 . At the present state, we refrained from more detailed analyses of the patients’ responses to different types of stimulation.…”

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

“…Section 3.2 ) that emphasize a network component as important for both structure and function of an epileptic brain network. Studies going beyond hubs or hub-like structures attribute a rather subordinate role to the epileptic focus and zones for seizure dynamics and for the many (patho-)physiologic phenomena seen in between seizures ( Geier et al, 2015a ; Geier et al, 2015b ; Geier and Lehnertz, 2017b ; Geier and Lehnertz, 2017a ; Bröhl and Lehnertz, 2019 ; Rings et al, 2019b ; Fruengel et al, 2020 ; Bröhl and Lehnertz, 2022 ).…”

“…In addition to these global aspects of time-evolving epileptic brain networks, several studies investigated the role that network vertices and edges play in seizure evolution ( Kramer et al, 2008 ; Wilke et al, 2011 ; Varotto et al, 2012 ; Burns et al, 2014 ; Geier et al, 2015a ; Zubler et al, 2015 ; Goodfellow et al, 2016 ; Geier and Lehnertz, 2017b ; Bröhl and Lehnertz, 2019 ; Bröhl and Lehnertz, 2022 ). Employing various centrality and other metrics to characterize a constituent’s importance for seizure dynamics, most studies reported these metrics to exhibit a high temporal variability as seizures evolve, both inter- and intraindividually.…”

Seizure forecasting: Where do we stand?

“…An in-depth investigation of the bridging dynamics is currently underway and employs novel, refined analysis techniques. 57 This can lead to an improved understanding of the complex spatial-temporal interaction phenomena preceding seizures in the large-scale epileptic brain network that cannot be captured by, for example, early warning indicators designed for simple one-dimensional systems. [58][59][60] Using another network-based approach to characterize the aforementioned pre-ictal phenomena, a measure of brain resilience developed recently.…”

“…Such a backbone‐like substructure emerges from brain regions (network nodes) that are usually deemed unaffected by the focal epileptic process but that act as bridges (groups of network links) between remote regions, that is, far off the seizure‐onset zone. An in‐depth investigation of the bridging dynamics is currently underway and employs novel, refined analysis techniques 57 . This can lead to an improved understanding of the complex spatial–temporal interaction phenomena preceding seizures in the large‐scale epileptic brain network that cannot be captured by, for example, early warning indicators designed for simple one‐dimensional systems 58–60 .…”