The correlation of metrics in complex networks with applications in functional brain networks

Li, C.; Wang, H.; Haan, Willem de; Stam, Cornelis J.; Mieghem, P.F.A. Van

doi:10.1088/1742-5468/2011/11/p11018

Cited by 74 publications

(63 citation statements)

References 54 publications

(113 reference statements)

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“…The measure M A,B (k) is different from the scalar correlation of topological metrics [39]. When we compare all the nodes (k = 100%), we have a full overlap and M A,B (100%) = 1.…”

Section: Definition 51 For Two Node Rankingsmentioning

confidence: 99%

Robustness envelopes of networks

Trajanovski

Martı́n-Hernández

Winterbach

et al. 2013

Journal of Complex Networks

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We study the robustness of networks under node removal, considering random node failure, as well as targeted node attacks based on network centrality measures. Whilst both of these have been studied in the literature, existing approaches tend to study random failure in terms of average-case behavior, giving no idea of how badly network performance can degrade purely by chance. Instead of considering average network performance under random failure, we compute approximate network performance probability density functions as functions of the fraction of nodes removed. We find that targeted attacks based on centrality measures give a good indication of the worst-case behavior of a network. We show that many centrality measures produce similar targeted attacks and that a combination of degree centrality and eigenvector centrality may be enough to evaluate worst-case behavior of networks. Finally, we study the robustness envelope and targeted attack responses of networks that are rewired to have high-and lowdegree assortativities, discovering that moderate assortativity increases confer more robustness against targeted attacks whilst moderate decreases confer more robustness against random uniform attacks.

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“…The measure M A,B (k) is different from the scalar correlation of topological metrics [39]. When we compare all the nodes (k = 100%), we have a full overlap and M A,B (100%) = 1.…”

Section: Definition 51 For Two Node Rankingsmentioning

confidence: 99%

Robustness envelopes of networks

Trajanovski

Martı́n-Hernández

Winterbach

et al. 2013

Journal of Complex Networks

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show abstract

“…It is very likely however, that these measures are highly correlated and can be replaced by a smaller number of more independent measures. A simulation study showed that most graph measures can be clustered into 2 to 4 groups, depending upon the topology of the underlying network (Li et al, 2011). For example, in the case of Erdős Rényi random graphs a strong correlation between the clustering coefficient and the average shortest path length can be expected.…”

Section: Conclusion and Future Prospectsmentioning

confidence: 99%

The trees and the forest: Characterization of complex brain networks with minimum spanning trees

Stam

Tewarie

Dellen

et al. 2014

International Journal of Psychophysiology

315

409

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In recent years there has been a shift in focus from the study of local, mostly task-related activation to the exploration of the organization and functioning of large-scale structural and functional complex brain networks. Progress in the interdisciplinary field of modern network science has introduced many new concepts, analytical tools and models which allow a systematic interpretation of multivariate data obtained from structural and functional MRI, EEG and MEG. However, progress in this field has been hampered by the absence of a simple, unbiased method to represent the essential features of brain networks, and to compare these across different conditions, behavioural states and neuropsychiatric/neurological diseases. One promising solution to this problem is to represent brain networks by a minimum spanning tree (MST), a unique acyclic subgraph that connects all nodes and maximizes a property of interest such as synchronization between brain areas. We explain how the global and local properties of an MST can be characterized. We then review early and more recent applications of the MST to EEG and MEG in epilepsy, development, schizophrenia, brain tumours, multiple sclerosis and Parkinson's disease, and show how MST characterization performs compared to more conventional graph analysis. Finally, we illustrate how MST characterization allows representation of observed brain networks in a space of all possible tree configurations and discuss how this may simplify the construction of simple generative models of normal and abnormal brain network organization.

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“…Similarly, every vertex in a tree graph has a depth. Selecting and studying graph properties of networks is a challenging problem as illustrated by Li et al [2011]. This chapter focuses on trees with specific graph properties that influence the performance of several distributed applications.…”

Section: Graph Properties and Applicationsmentioning

confidence: 99%

Multi-level reconfigurable self-organization in overlay services

Pournaras¹

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The correlation of metrics in complex networks with applications in functional brain networks

Cited by 74 publications

References 54 publications

Robustness envelopes of networks

Robustness envelopes of networks

The trees and the forest: Characterization of complex brain networks with minimum spanning trees

Multi-level reconfigurable self-organization in overlay services

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