Centrality-based identification of important edges in complex networks

Bröhl, Timo; Lehnertz, Klaus

doi:10.1063/1.5081098

Cited by 45 publications

(53 citation statements)

References 81 publications

(81 reference statements)

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“…Our study revealed that predictive nodes are not the most central nodes in an evolving epileptic network, but we cannot yet make a similar statement for predictive edges. Recent modifications of centrality concepts for nodes to those for edges 59 are expected to provide further insights into the role of network edges and nodes in ictogenesis.…”

Section: Discussionmentioning

confidence: 99%

Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks

Rings

Wrede

Lehnertz

2019

Sci Rep

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Knowing when, where, and how seizures are initiated in large-scale epileptic brain networks remains a widely unsolved problem. Seizure precursors – changes in brain dynamics predictive of an impending seizure – can now be identified well ahead of clinical manifestations, but either the seizure onset zone or remote brain areas are reported as network nodes from which seizure precursors emerge. We aimed to shed more light on the role of constituents of evolving epileptic networks that recurrently transit into and out of seizures. We constructed such networks from more than 3200 hours of continuous intracranial electroencephalograms recorded in 38 patients with medication refractory epilepsy. We succeeded in singling out predictive edges and predictive nodes. Their particular characteristics, namely edge weight respectively node centrality (a fundamental concept of network theory), from the pre-ictal periods of 78 out of 97 seizures differed significantly from the characteristics seen during inter-ictal periods. The vast majority of predictive nodes were connected by most of the predictive edges, but these nodes never played a central role in the evolving epileptic networks. Interestingly, predictive nodes were entirely associated with brain regions deemed unaffected by the focal epileptic process. We propose a network mechanism for a transition into the pre-seizure state, which puts into perspective the role of the seizure onset zone in this transition and highlights the necessity to reassess current concepts for seizure generation and seizure prevention.

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Section: Discussionmentioning

confidence: 99%

Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks

Rings

Wrede

Lehnertz

2019

Sci Rep

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“…It is conceivable that there is a high inter-individual variation in pre-seizure period duration, which the variation in prodromal symptom onset and duration seems to support 39 . Finally, the results of this study should be combined with those of similar studies focusing on edges rather than nodes 19 , which could be expanded to include novel edge centrality indices 40 . Previous studies have assessed whether predictive edges connect predictive nodes 14 , reporting that this occurs in a majority of cases.…”

Section: Discussionmentioning

confidence: 99%

Reconfiguration of human evolving large-scale epileptic brain networks prior to seizures: an evaluation with node centralities

Fruengel

Bröhl

Rings

et al. 2020

Sci Rep

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Previous research has indicated that temporal changes of centrality of specific nodes in human evolving large-scale epileptic brain networks carry information predictive of impending seizures. Centrality is a fundamental network-theoretical concept that allows one to assess the role a node plays in a network. This concept allows for various interpretations, which is reflected in a number of centrality indices. Here we aim to achieve a more general understanding of local and global network reconfigurations during the pre-seizure period as indicated by changes of different node centrality indices. To this end, we investigate—in a time-resolved manner—evolving large-scale epileptic brain networks that we derived from multi-day, multi-electrode intracranial electroencephalograpic recordings from a large but inhomogeneous group of subjects with pharmacoresistant epilepsies with different anatomical origins. We estimate multiple centrality indices to assess the various roles the nodes play while the networks transit from the seizure-free to the pre-seizure period. Our findings allow us to formulate several major scenarios for the reconfiguration of an evolving epileptic brain network prior to seizures, which indicate that there is likely not a single network mechanism underlying seizure generation. Rather, local and global aspects of the pre-seizure network reconfiguration affect virtually all network constituents, from the various brain regions to the functional connections between them.

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“…An eigenvector centrality for edges can be developed by considering the line graph and its adjacency matrix A (e) [11]. In this setting, A (e) ∈ R m×m has A (e) e 1 ,e 2 = 0 if and only if e 1 ∈ E and e 2 ∈ E share at least one node.…”

Section: Eigenvector Centrality For Nodes and Edgesmentioning

confidence: 99%

Node and Edge Eigenvector Centrality for Hypergraphs

Tudisco

Higham

2021

Preprint

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Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting directly for higher order interactions, notably through a hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define and analyze a class of spectral centrality measures for identifying important nodes and hyperedges in hypergraphs, generalizing existing network science concepts. By exploiting the latest developments in nonlinear Perron-Frobenius theory, we show how the resulting constrained nonlinear eigenvalue problems have unique solutions that can be computed efficiently via a nonlinear power method iteration. We illustrate the measures on realistic data sets.

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Centrality-based identification of important edges in complex networks

Cited by 45 publications

References 81 publications

Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks

Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks

Reconfiguration of human evolving large-scale epileptic brain networks prior to seizures: an evaluation with node centralities

Node and Edge Eigenvector Centrality for Hypergraphs

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