Emergence of biconnected clusters in explosive percolation

Abstract

By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intra-cluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters. However, the volume fractal dimension $d_f^{\prime }$ of biconnected clusters varies depending on the competition rules of intra-cluster bonds. The size distribution of biconnected clusters exhibits double-scaling behavior: large clusters follow the standard Fisher exponent derived from the hyperscaling relation ${\tau }^{\prime }=1+1/d_f^{\prime }$, while small clusters display a modified Fisher exponent ${\tau }_0<{\tau }^{\prime }$. These findings provide insights into the intricate nature of connectivity in explosive percolation.

9 pages, 8 figures

References in corpus (37)

• Higher-order organization of complex networks
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Percolation on complex networks: Theory and application
• "Explosive Percolation" Transition is Actually Continuous
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Explosive Phenomena in Complex Networks
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive Percolation: Novel critical and supercritical phenomena
• Construction and Analysis of Random Networks with Explosive Percolation
• Immunization and targeted destruction of networks using explosive percolation
• Core percolation on complex networks
• Articulation Points in Complex Networks
• Kinetic Theory of Random Graphs: from Paths to Cycles
• A new route to Explosive Percolation
• Continuity of the Explosive Percolation Transition
• Bicomponents and the robustness of networks to failure
• Tricritical point in heterogeneous k-core percolation
• Using explosive percolation in analysis of real-world networks
• Suppression effect on explosive percolations
• Clique percolation in random graphs
• Identifying vital nodes by Achlioptas process
• Critical percolation clusters in seven dimensions and on a complete graph
• Scaling for the Percolation Backbone
• Geometric structure of percolation clusters
• Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble
• Criterion for explosive percolation transitions on complex networks
• Scaling of cluster heterogeneity in percolation transitions
• No-enclave percolation corresponds to holes in the cluster backbone
• Hysteretic percolation from locally optimal individual decisions
• k-core structure of real multiplex networks
• Cluster-size heterogeneity in the two-dimensional Ising model
• Universality class of epidemic percolation transitions driven by random walks
• Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model
• Leaf-excluded percolation in two and three dimensions

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