Random walks and Laplacians on hypergraphs: When do they match?

Mulas, Raffaella; Kuehn, Christian; Böhle, Tobias; Jost, Jürgen

doi:10.1016/j.dam.2022.04.009

Cited by 11 publications

(2 citation statements)

References 38 publications

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“…Several studies have shown that the presence of higher-order interactions may severely affect the dynamics of network systems, from diffusion [26,27] and synchronization [28,29] to social [30][31][32][33] and evolutionary processes [34], possibly leading to the emergence of abrupt (explosive) transitions between states. Under different mechanisms of simple and complex contagion, the presence of higher-order structures can make the propagation process on the network significantly different [35][36][37][38].…”

Section: Effect Of the Higher-order Structure On The Propagation Dyna...mentioning

confidence: 99%

Identifying influential nodes in complex contagion mechanism

Song

Wang

2023

Front. Phys.

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Identifying influential nodes in complex networks is one of the most important and challenging problems to help optimize the network structure, control the spread of the epidemic and accelerate the spread of information. In a complex network, the node with the strongest propagation capacity is known as the most influential node from the perspective of propagation. In recent years, identifying the key nodes in complex networks has received increasing attention. However, it is still a challenge to design a metric that has low computational complexity but can accurately identify important network nodes. Currently, many centrality metrics used to evaluate the influence capability of nodes cannot balance between high accuracy and low time complexity. Local centrality suffers from accuracy problems, while global metrics require higher time complexity, which is inefficient for large scale networks. In contrast, semi-local metrics are with higher accuracy and lower time cost. In this paper, we propose a new semi-local centrality measure for identifying influential nodes under complex contagion mechanisms. It uses the higher-order structure within the first and second-order neighborhoods of nodes to define the importance of nodes with near linear time complexity, which can be applied to large-scale networks. To verify the accuracy of the proposed metric, we simulated the disease propagation process in four real and two artificial networks using the SI model under complex propagation. The simulation results show that the proposed method can identify the nodes with the strongest propagation ability more effectively and accurately than other current node importance metrics.

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Section: Effect Of the Higher-order Structure On The Propagation Dyna...mentioning

confidence: 99%

Identifying influential nodes in complex contagion mechanism

Song

Wang

2023

Front. Phys.

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“…Unlike the situation in graphs where the random walk process is uniquely determined by the adjacency matrix, there are multiple ways to define random walks on hypergraphs. In the present work we consider the random walk in its simplest form [13]. (i) A random walker sitting at vertex i first walks to an incident hyperedge e with equal probability.…”

Section: Hyperlink Predictionmentioning

confidence: 99%

Hyperlink prediction via local random walks and Jensen–Shannon divergence

Xu¹,

Deng²,

Zhang³

2023

J. Stat. Mech.

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Many real-world systems involving higher-order interactions can be modeled by hypergraphs, where vertices represent the systemic units and hyperedges describe the interactions among them. In this paper, we focus on the problem of hyperlink prediction which aims at inferring missing hyperlinks based on observed hyperlinks. We propose three similarity indices for hyperlink prediction based on local random walks and Jensen–Shannon divergence. Numerical experiments show that the proposed indices outperform the state-of-the-art methods on a broad range of datasets.

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