Hcore-Init: Neural Network Initialization based on Graph Degeneracy

Limnios, Stratis; Dasoulas, George; Thilikos, Dimitrios M.; Vazirgiannis, Michalis

doi:10.1109/icpr48806.2021.9412940

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…The (k, m)-hypercore is defined as the maximum subhypergraph J induced by the set of nodes A V and with hyperedges of size at least m, such that 8 i 2 A, D J m ðiÞ ≥ k, where D J m ðiÞ denotes the number of distinct hyperedges of size at least m in which i is involved within the subhypergraph J 40 . In other terms, all the nodes in the (k, m)-hypercore belong to at least k hyperedges of size at least m, within the hypercore itself.…”

Section: Hyper-core Decomposition and Hypercorenessmentioning

confidence: 99%

“…The (k, m) two-mode-core of a bipartite graph corresponds indeed to the bipartite subgraphs in which the nodes have degree respectively at least m (for the nodes representing hyperedges) and k (for the nodes representing nodes of the hypergraph). The earlier works introducing such concepts [21][22][23] have indeed mostly focused on their interpretation in bipartite networks, rather than for hypergraphs (see however 40 ), and have shown their interest for visualisation purposes 21 but did not study how empirical data can be systematically decomposed into hypercores, nor the interplay between hyper-cores and dynamical processes on hypergraphs.…”

Section: Hyper-core Decomposition and Hypercorenessmentioning

confidence: 99%

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Hyper-cores promote localization and efficient seeding in higher-order processes

Mancastroppa,

Iacopini,

Petri

et al. 2023

Nat Commun

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Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.

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Section: Hyper-core Decomposition and Hypercorenessmentioning

confidence: 99%

Section: Hyper-core Decomposition and Hypercorenessmentioning

confidence: 99%

Hyper-cores promote localization and efficient seeding in higher-order processes

Mancastroppa,

Iacopini,

Petri

et al. 2023

Nat Commun

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show abstract

“…Networks in which modules or communities have a sparse interaction with nodes belonging to different communities represent a feature of many real systems. Furthermore in some models in ecology (plants-pollinators-insects) [13,14] and in deep learning [15], the interactions among the nodes belonging to the same community are absent or irrelevant; this property is called disassortative and the associated graph of interactions is multipartite.…”

Section: Introductionmentioning

confidence: 99%