General theory for extended-range percolation on simple and multiplex networks
arXiv:2407.04585 · doi:10.1103/PhysRevE.110.034302
Abstract
Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally tree-like. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram merges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte-Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.
arXiv comment21 pages, 9 figures
References in corpus (46)
- Catastrophic cascade of failures in interdependent networks
- Multilayer Networks
- The structure and dynamics of multilayer networks
- Critical phenomena in complex networks
- Advances in Quantum Cryptography
- Robustness and resilience of complex networks
- Avalanche Collapse of Interdependent Network
- Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
- Percolation on complex networks: Theory and application
- Phase Transitions in the Coloring of Random Graphs
- Percolation on sparse networks
- End-to-end capacities of a quantum communication network
- Percolation Theory on Interdependent Networks Based on Epidemic Spreading
- Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
- Redundant interdependencies boost the robustness of multilayer networks
- Quantum complex networks
- Implementation of a 46-node quantum metropolitan area network
- Message passing theory for percolation models on multiplex networks with link overlap
- Higher-order percolation processes on multiplex hypergraphs
- Link overlap, viability, and mutual percolation in multiplex networks
- Entanglement Distribution in Pure-State Quantum Networks
- Recent advances of percolation theory in complex networks
- The dynamic nature of percolation on networks with triadic interactions
- Long-range big quantum-data transmission
- Belief propagation for networks with loops
- The theory of percolation on hypergraphs
- Complex Quantum Networks: a Topical Review
- Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs
- Message passing methods on complex networks
- Robustness of Noisy Quantum Networks
- Concurrence Percolation in Quantum Networks
- Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
- Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
- Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
- Bond percolation on simple cubic lattices with extended neighborhoods
- Cumulative Merging Percolation and the epidemic transition of the Susceptible-Infected-Susceptible model in networks
- Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone
- Site percolation thresholds on triangular lattice with complex neighborhoods
- Color-avoiding percolation
- Shortest-path percolation on random networks
- Optimal redundancy against disjoint vulnerabilities in networks
- Extended-range percolation in complex networks
- Heterogeneous message passing for heterogeneous networks
- Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods
- No-exclaves percolation on random networks
- Cumulative Merging Percolation: A long-range percolation process in networks