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Traditional node-based dismantling strategies, which remove nodes along with their associated edges, tend to incur high costs. In contrast, edge-based strategies are more cost-effective but often suffer from low efficiency due to the large number of edges in most networks. To address these challenges, we propose a divide-and-conquer framework that reinterprets network-level dismantling as cluster-level dismantling. Specifically, we integrate community detection with explosive percolation to develop the Community-based Edge Percolation (CEP) algorithm, which targets critical edges whose removal effectively breaks the network into subcritical components, thereby optimizing dismantling efficiency while minimizing costs. Experiments on 38 synthetic networks derived from four different models, as well as on nine empirical networks, show that CEP consistently outperforms state-of-the-art (SOTA) algorithms across nearly all datasets, yielding improvements of up to 30.611 % in f c and 67.108 % in Schneider R . Further analysis indicates that the sets of removed edges identified by CEP have a low correlation with those identified by other benchmarks, underlining its novelty and superior capability in identifying critical edges. Overall, we propose a universal and efficient edge dismantling framework that exhibits substantial advantages in large-scale empirical networks, offering valuable insights into network robustness.
Phase transitions in the node, edge, bootstrap, and diffusion percolation models on the Sierpiński carpet
Phase transitions in the node, edge, bootstrap, and diffusion percolation models on the Sierpiński carpet
18On Percolation and the Bunkbed Conjecture
We study a problem on edge percolation on product graphsG×K2. HereGis any finite graph andK2consists of two vertices {0, 1} connected by an edge. Every edge inG×K2is present with probabilitypindependent of other edges. The bunkbed conjecture states that for allGandp, the probability that (u, 0) is in the same component as (v, 0) is greater than or equal to the probability that (u, 0) is in the same component as (v, 1) for every pair of verticesu,v∈G.We generalize this conjecture and formulate and prove similar statements for randomly directed graphs. The methods lead to a proof of the original conjecture for special classes of graphsG, in particular outerplanar graphs.
Read more24On the Bogomolny–Schmit conjecture
Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer experiments showed that the mean number of clusters per vertex and the mean number of nodal domains per unit area are very close but different. Since the original argument was mostly supported by numerics, it was believed that the percolation model is wrong. In this paper we give some numerical evidence in favour of the percolation model.
Read moreCommentary to: Oriented Percolation in One-Dimension 1/|x−y|2 Percolation Models
The main result of the article (Theorem 1.1) is the occurrence of oriented percolation for the independent edge percolation model on Z, with occupation probabilities p{x,y} = 1 − exp(−β/|x − y|2) if |x − y| > 1 and p{x,x+1} = p, for β > 1 and p sufficiently close to one. Together with FKG inequalities this has implications for the Ising model, as stated in Corollary 1.2. It should be added that the content of Corollary 1.2 is an immediate consequence of Theorem 3.4, Sect. 3(ii) in [1], with the result holding even for β > 1. This fact was missed by the authors at the time the article was written. We take the opportunity for adding a minor correction: at Remark 1, following Theorem 1.1, instead of “β replaced by β ′ ≥ κβ .” one should read “β replaced by β ′ ≥ κβ and p similarly replaced by p′ = 1 − (1 − p) ′/β .” (That is, writing p = 1 − e−βJ in the first line of (1.1) we replace β by β ′.)
Read more10Info2vec: An aggregative representation method in multi-layer and heterogeneous networks
Info2vec: An aggregative representation method in multi-layer and heterogeneous networks
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