Multiple percolation transitions in a configuration model of network of networks

Abstract

Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually connected component when a fraction of nodes have been removed from these networks. Here we characterize the emergence of the mutually connected component in a network of networks in which every node of a network (layer) $\alpha$ is connected with $q_{\alpha }$ randomly chosen replicas in some other networks and is interdependent of these nodes with probability $r$. We find that when the superdegrees $q_{\alpha }$ of different layers in the network of networks are distributed heterogeneously, multiple percolation phase transition can occur, and depending on the value of $r$ these transition are continuous or discontinuous.

(11 pages, 4 figures)

References in corpus (4)

• Critical phenomena in complex networks
• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Emergence of network features from multiplexity

Cited by in corpus (57)

• Influence maximization in complex networks through optimal percolation
• Evolutionary games on multilayer networks: A colloquium
• The physics of spreading processes in multilayer networks
• Percolation on complex networks: Theory and application
• Avoiding catastrophic failure in correlated networks of networks
• Measuring and modelling correlations in multiplex networks
• Explosive Phenomena in Complex Networks
• The synchronized dynamics of time-varying networks
• Synchronization in networks with multiple interaction layers
• Towards real-world complexity: an introduction to multiplex networks
• Redundant interdependencies boost the robustness of multilayer networks
• Cascading Failures in Complex Networks
• Eradicating Catastrophic Collapse in Interdependent Networks via Reinforced Nodes
• Higher-order percolation processes on multiplex hypergraphs
• Message passing theory for percolation models on multiplex networks with link overlap
• Optimal percolation on multiplex networks
• Interdisciplinary and physics challenges of Network Theory
• Bond percolation on multiplex networks
• Control of Multilayer Networks
• Correlated Edge Overlaps in Multiplex Networks
• Functional Multiplex PageRank
• Non-linear growth and condensation in multiplex networks
• Group percolation in interdependent networks
• Extracting Information from Multiplex Networks
• The interdependent network of gene regulation and metabolism is robust where it needs to be
• Mutually connected component of network of networks with replica nodes
• Cascading failures in interdependent systems under a flow redistribution model
• Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds
• Competing contagion processes: Complex contagion triggered by simple contagion
• Epidemic spreading and bond percolation in multilayer networks
• Strength of weak layers in cascading failures on multiplex networks: case of the international trade network
• Multiplex networks with heterogeneous activities of the nodes
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Fluctuations in percolation of sparse complex networks
• Controlling the uncertain response of real multiplex networks to random damage
• Percolation in real multiplex networks
• How does bond percolation happen in coloured networks?
• Nonbacktracking expansion of finite graphs
• Clustering determines the dynamics of complex contagions in multiplex networks
• Giant components in directed multiplex networks
• Correlations between weights and overlap in ensembles of weighted multiplex networks
• Cascading failures in interdependent networks with finite functional components
• Cascading failures in coupled networks with both inner-dependency and inter-dependency links
• General and exact approach to percolation on random graphs
• Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem
• Percolation on branching simplicial and cell complexes and its relation to interdependent percolation
• Competition between global and local online social networks
• Highly Clustered Complex Networks in the Configuration Model: Random Regular Small-World Network
• Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions
• Dependency-based targeted attacks in interdependent networks
• Percolation of networks with directed dependency links
• Statistical mechanics of bipartite $z$-matchings
• Multiple structural transitions in interacting networks
• Exploring Percolative Landscapes: Infinite Cascades of Geometric Phase Transitions
• Observability transition in multiplex networks
• Diffusion dynamics and synchronizability of hierarchical products of networks
• Queues on interacting networks