Quantifying Disorder in Networks

Passerini, Filippo; Severini, Simone

doi:10.4018/978-1-60960-171-3.ch005

Cited by 6 publications

(6 citation statements)

References 24 publications

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“…It has been recently shown that the Von Neumann entropy can also be used to characterize (single layer) graphs 31,32 . Given a graph G represented by the adjacency matrix A, the Von Neumann entropy of G is defined as the Shannon entropy of the spectrum of the rescaled combinatorial Laplacian L G associated to G (see Methods).…”

Section: Resultsmentioning

confidence: 99%

Structural reducibility of multilayer networks

et al. 2015

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Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.

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Section: Resultsmentioning

confidence: 99%

Structural reducibility of multilayer networks

et al. 2015

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“…Here,

0

if there is correlation between ROIs i and j in the frequency band represented by α. The Von Neumann entropy (Braunstein et al, 2006 ; Passerini and Severini, 2010 ) of the corresponding complex network is defined by

where

[α] = c × ( S [α] − A [α] ) is the combinatorial Laplacian rescaled by

, and S is the diagonal matrix of the strengths of the nodes. From the eigen-decomposition of the Laplacian, it is possible to show that the entropy can be calculated by

where

are the eigenvalues of

[α] .…”

Section: Methodsmentioning

confidence: 99%

Mapping Multiplex Hubs in Human Functional Brain Networks

2016

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Typical brain networks consist of many peripheral regions and a few highly central ones, i.e., hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches.

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“…This is consistently true for both null models, and for the three types of networks that had a sufficient sample size. Previous work on random networks (using a model that is essentially the Type I null model) shows that sufficiently large networks achieve maximal von Neuman entropy (Du et al, 2010;Passerini and Severini, 2011). In Figure 8, we compare the logistic of z i to the richness of the network.…”

Section: Larger Network Are Less Complex Than They Could Bementioning

confidence: 98%

SVD Entropy Reveals the High Complexity of Ecological Networks

2021

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Quantifying the complexity of ecological networks has remained elusive. Primarily, complexity has been defined on the basis of the structural (or behavioural) complexity of the system. These definitions ignore the notion of “physical complexity,” which can measure the amount of information contained in an ecological network, and how difficult it would be to compress. We present relative rank deficiency and SVD entropy as measures of “external” and “internal” complexity, respectively. Using bipartite ecological networks, we find that they all show a very high, almost maximal, physical complexity. Pollination networks, in particular, are more complex when compared to other types of interactions. In addition, we find that SVD entropy relates to other structural measures of complexity (nestedness, connectance, and spectral radius), but does not inform about the resilience of a network when using simulated extinction cascades, which has previously been reported for structural measures of complexity. We argue that SVD entropy provides a fundamentally more “correct” measure of network complexity and should be added to the toolkit of descriptors of ecological networks moving forward.

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Quantifying Disorder in Networks

Cited by 6 publications

References 24 publications

Structural reducibility of multilayer networks

Structural reducibility of multilayer networks

Mapping Multiplex Hubs in Human Functional Brain Networks

SVD Entropy Reveals the High Complexity of Ecological Networks

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