Centrality measures in simplicial complexes: Applications of topological data analysis to network science

Serrano, Daniel Hernández; Gómez, Darío Sánchez

doi:10.1016/j.amc.2020.125331

Cited by 22 publications

(9 citation statements)

References 25 publications

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“…We follow a procedure to encode the resulting k-uniform hypergraph as an “hyper-adjacency matrix.” Among the multiple alternatives [33], the one used in this work inherits the lower adjacency matrix representation of simplicial complexes into uniform hypergraphs, which was also recently adapted to develop vector centralities on hypergraphs [41]. Put simply, two hyperedges of dimension k are connected if they share an hyperedge of dimension k – 1 [33, 34, 42]. For example, two triangles are connected if they have an edge in common.…”

Section: Methodsmentioning

confidence: 99%

Emergence of High-Order Functional Hubs in the Human Brain

Santos

Tewarie

Baudot³

et al. 2023

Preprint

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Network theory is often based on pairwise relationships between nodes, which is not necessarily realistic for modeling complex systems. Importantly, it does not accurately capture non-pairwise interactions in the human brain, often considered one of the most complex systems. In this work, we develop a multivariate signal processing pipeline to build high-order networks from time series and apply it to resting-state functional magnetic resonance imaging (fMRI) signals to characterize high-order communication between brain regions. We also propose connectivity and signal processing rules for building uniform hypergraphs and argue that each multivariate interdependence metric could define weights in a hypergraph. As a proof of concept, we investigate the most relevant three-point interactions in the human brain by searching for high-order "hubs" in a cohort of 100 individuals from the Human Connectome Project. We find that, for each choice of multivariate interdependence, the high-order hubs are compatible with distinct systems in the brain. Additionally, the high-order functional brain networks exhibit simultaneous integration and segregation patterns qualitatively observable from their high-order hubs. Our work hereby introduces a promising heuristic route for hypergraph representation of brain activity and opens up exciting avenues for further research in high-order network neuroscience and complex systems.

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Section: Methodsmentioning

confidence: 99%

Emergence of High-Order Functional Hubs in the Human Brain

Santos

Tewarie

Baudot³

et al. 2023

Preprint

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“…However, it is already possible to use these metrics to differentiate groups [26,64], and plausible to assume that the interpretation of some classical metrics could be extrapolated to higher orders interactions. For example, the concept of the centralities using pair-wise interactions is used to understand node importance and hubs, the same, in theory, could be applied to the relationships between 3 or more vertices by extending the definition of centrality from networks to simplicial complexes, as done in [88,89].…”

Section: Discussionmentioning

confidence: 99%

A hands-on tutorial on network and topological neuroscience

Centeno

Moreni

Vriend

et al. 2021

Preprint

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The brain is an extraordinarily complex system that facilitates the efficient integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pair-wise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks, and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses data from the 1000 Functional Connectomes Project. Moreover, we would like to highlight one part of our notebook that is solely dedicated to realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pair-wise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

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“…Hypergraphs have attracted considerable interest from the research community as a generalization of networks due to their capability of encoding higher-order interactions between more than two agents [25][26][27][28]. The recently introduced s-SIS model [39] was introduced as a complex contagion model in simplicial complexes and hypergraphs and has attracted extensive interest due to its simplicity, analytic tractability, and novel critical phenomena [40][41][42].…”

Section: Modelmentioning

confidence: 99%

“…A hypergraph is a generalization of network that can describe higher-order interactions between more than two agents, which widely appear in both natural and social systems, that networks cannot [25][26][27][28]. A hypergraph consists of nodes and hyperedges, and a hyperedge of size d connects d nodes simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Effective epidemic containment strategy in hypergraphs

Jhun

2021

Preprint

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Recently, hypergraphs have attracted considerable interest from the research community as a generalization of network capable of encoding higher-order interactions, which commonly appear in both natural and social systems. Epidemic dynamics in hypergraphs has been studied by using simplicial susceptible-infectedsusceptible (s-SIS) model; however, the efficient immunization strategy for epidemics in hypergraphs is not studied despite the importance of the topic in mathematical epidemiology. Here, we propose an immunization strategy that immunizes hyperedges with high simultaneous infection probability (SIP). This strategy can be implemented in general hypergraphs. We also generalize the edge epidemic importance (EI)-based immunization strategy, which is the state-of-the-art in complex network. However, it does not perform as well as the SIP-based method in hypergraphs despite its high computational cost. We also show that immunizing hyperedges with high H-eigenscore effectively contains the epidemics in uniform hypergraphs. A high SIP of a hyperedge suggests that the hyperedge is a 'hotspot' of the epidemic process. Therefore, SIP can be used as a centrality measure to quantify a hyperedge's influence on higher-order dynamics in general hypergraphs. The effectiveness of the immunization strategies suggests the necessity of scientific, data-driven, systematic policy-making for epidemic containment.

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Centrality measures in simplicial complexes: Applications of topological data analysis to network science

Cited by 22 publications

References 25 publications

Emergence of High-Order Functional Hubs in the Human Brain

Emergence of High-Order Functional Hubs in the Human Brain

A hands-on tutorial on network and topological neuroscience

Effective epidemic containment strategy in hypergraphs

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