Randomizing hypergraphs preserving degree correlation and local clustering

Nakajima, Koji; Shudo, Kazuyuki; Masuda, Naoki

doi:10.48550/arxiv.2106.12162

Cited by 3 publications

(4 citation statements)

References 72 publications

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“…To detect non-trivial temporal and topological patterns of events, we compare properties obtained from real-world higher-order temporal networks with those of designed null models. We generalize the randomized reference models of pairwise evolving networks which gradually preserve and destroy temporal and topological properties of pairwise interactions [25][26][27] for higher-order temporal networks. Given a higher-order evolving network H and any given order d of events, we introduce 3 randomized null models H 1 d , H 2 d and H 3 d which systematically randomize order d events only, without changing events of any other order d ′ � = d .…”

Section: Network Randomization-control Methodsmentioning

confidence: 99%

Temporal-topological properties of higher-order evolving networks

Ceria

Wang

2023

Sci Rep

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Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more than two people. Such group interactions can be represented as higher-order events of an evolving network. Here, we propose methods to characterize the temporal-topological properties of higher-order events to compare networks and identify their (dis)similarities. We analyzed 8 real-world physical contact networks, finding the following: (a) Events of different orders close in time tend to be also close in topology; (b) Nodes participating in many different groups (events) of a given order tend to involve in many different groups (events) of another order; Thus, individuals tend to be consistently active or inactive in events across orders; (c) Local events that are close in topology are correlated in time, supporting observation (a). Differently, in 5 collaboration networks, observation (a) is almost absent; Consistently, no evident temporal correlation of local events has been observed in collaboration networks. Such differences between the two classes of networks may be explained by the fact that physical contacts are proximity based, in contrast to collaboration networks. Our methods may facilitate the investigation of how properties of higher-order events affect dynamic processes unfolding on them and possibly inspire the development of more refined models of higher-order time-varying networks.

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Section: Network Randomization-control Methodsmentioning

confidence: 99%

Temporal-topological properties of higher-order evolving networks

Ceria

Wang

2023

Sci Rep

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“…To detect non-trivial temporal and topological patterns of events, we compare properties obtained from real-world higher-order temporal networks with those of designed null models. We generalize the randomized reference models of pairwise evolving networks which gradually preserve and destroy temporal and topological properties of pairwise interactions [25][26][27] for higher-order temporal networks. Given a higher-order evolving network H and any given order d of events, we introduce 3 randomized null models H 1 d , H 2 d and H 3 d which systematically remove or preserve specific temporal or topological properties of order d events only, while preserving the properties of events of any other size d = d. We denote as E d the set of events with the same size d. Randomized network H 1 d is obtained by randomly re-shuffling the time stamps of the events in E d , without changing the topological locations of these events.…”

Section: Network Randomization -Control Methodsmentioning

confidence: 99%

Topological–temporal properties of evolving networks

Ceria

Havlin²,

Hanjalic³

et al. 2022

Journal of Complex Networks

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Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare different real-world networks and to detect their common patterns or differences. A systematic method that can characterize simultaneously the temporal and topological relations of the time-specific interactions (also called contacts or events) of a temporal network, is still missing. In this article, we propose a method to characterize to what extent contacts that happen close in time occur also close in topology. Specifically, we study the interrelation between temporal and topological properties of the contacts from three perspectives: (1) the correlation (among the elements) of the activity time series which records the total number of contacts in a network that happen at each time step; (2) the interplay between the topological distance and time difference of two arbitrary contacts; (3) the temporal correlation of contacts within the local neighbourhood centred at each link (so-called ego-network) to explore whether such contacts that happen close in topology are also close in time. By applying our method to 13 real-world temporal networks, we found that temporal–topological correlation of contacts is more evident in virtual contact networks than in physical contact networks. This could be due to the lower cost and easier access of online communications than physical interactions, allowing and possibly facilitating social contagion, that is, interactions of one individual may influence the activity of its neighbours. We also identify different patterns between virtual and physical networks and among physical contact networks at, for example, school and workplace, in the formation of correlation in local neighbourhoods. Patterns and differences detected via our method may further inspire the development of more realistic temporal network models, that could reproduce jointly temporal and topological properties of contacts.

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“…Given the recent interest towards such objects, the definition of analytical tools to study them is still in its infancy [6][7][8]. The present paper represents our contribution to fill this gap: hereby, we extend the class of entropy-based null models [9,10] to hypergraphs.…”

mentioning

confidence: 99%

“…Early attempts to define randomisation models for hypergraphs can be found in [20]: there, however, the authors have just considered hyperedges that are incident to triples of nodes; the same framework has been applied to study the World Trade Network [7]. Considering the incidence matrix has, however, two clear advantages: (i) generality, because the incidence matrix allows hyperedges of any size to be handled at once; (ii) compactness, because the order of tensor I never exceeds two and allows any hypergraph to be represented as a traditional, bipartite graph -the two layers of the latter being now defined by nodes and hyperedges [7].…”

mentioning

confidence: 99%

Entropy-based random models for hypergraphs

Saracco¹,

Petri²,

Lambiotte³

et al. 2022

Preprint

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Network science has traditionally focused on pairwise relationships while disregarding many-body interactions. Hypergraphs are promising mathematical objects for the description of the latter ones. Here, we propose null models to analyse hypergraphs that generalise the classical Erdös-Rényi and Configuration Model by randomising incidence matrices in a constrained fashion. After discussing them, we extend the definition of several network quantities to hypergraphs, derive their expected values and compare them with empirical ones, to detect significant deviations from random behaviours.

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Randomizing hypergraphs preserving degree correlation and local clustering

Cited by 3 publications

References 72 publications

Temporal-topological properties of higher-order evolving networks

Temporal-topological properties of higher-order evolving networks

Topological–temporal properties of evolving networks

Entropy-based random models for hypergraphs

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