Son, Grassberger, and Paczuski Reply:

Son, Seung‐Woo; Grassberger, Peter; Paczuski, Maya

doi:10.1103/physrevlett.111.189602

Cited by 45 publications

(108 citation statements)

References 5 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…The models studied in [7,[24][25][26][27][32][33][34][35][36][37][38][39][40][41][42][43] were originally presented as interdependent networks showing failure cascades subsequent to random removal of nodes, but as noted in [24,27] they are more easily interpreted as single multiplex networks. More precisely, while in general interdependent networks some nodes depend on each other, these dependencies always were assumed in most of these papers to be pairwise and mutual.…”

Section: The Model Its Mapping Onto Sos Type Growth and The Resmentioning

confidence: 99%

“…The fact that network topology can change the critical behavior entirely was demonstrated recently [12] for cooperative spreading agents (so-called syndemics or co-infections). Another warning should be the fact that interdependent two-and three-dimensional lattices do not show the first order transition found on random networks, but show second order transitions [27], if all links are short range.…”

Section: Introductionmentioning

confidence: 99%

“…While there exist very efficient methods for OP and for all versions of cooperative percolation, this is not the case for the class of models introduced in [7] and developed further in [24][25][26][27][32][33][34][35][36][37][38][39][40][41][42][43]. For these models which can either be viewed as describing cascading failures on interdependent networks or viable clusters on multiplex networks, the algorithms used so far in large simulations are extremely slow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and solid-on-solid surface growth

Grassberger

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

The "SOS" in the title does not refer to the international distress signal, but to "solid-on-solid" (SOS) surface growth. The catastrophic cascades are those observed by Buldyrev et al. in interdependent networks, which we re-interpret as multiplex networks with agents that can only survive if they mutually support each other, and whose survival struggle we map onto an SOS type growth model. This mapping not only reveals non-trivial structures in the phase space of the model, but also leads to a new and extremely efficient simulation algorithm. We use this algorithm to study interdependent agents on duplex Erdös-Rényi (ER) networks and on lattices with dimensions 2, 3, 4, and 5. We obtain new and surprising results in all these cases, and we correct statements in the literature for ER networks and for 2-d lattices. In particular, we find that d = 4 is the upper critical dimension, that the percolation transition is continuous for d ≤ 4 but -at least for d = 3 -not in the universality class of ordinary percolation. For ER networks we verify that the cluster statistics is exactly described by mean field theory, but find evidence that the cascade process is not. For d = 5 we find a first order transition as for ER networks, but we find also that small clusters have a nontrivial mass distribution that scales at the transition point. Finally, for d = 2 with intermediate range dependency links we propose a scenario different from that proposed in W. Li et al., PRL 108, 228702 (2012).

show abstract

Section: The Model Its Mapping Onto Sos Type Growth and The Resmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and solid-on-solid surface growth

Grassberger

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…We find a non-trivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases.Previous studies of the robustness of interdependent networks have focused on networks in which there is no constraint on the distance between the interdependent nodes [1][2][3][4][5][6][7][8][9]. However, many dependency links in the real world connect nearby nodes.…”

mentioning

confidence: 99%

“…Previous studies of interdependent networks have used this equation [9], often modifying either the value of p [1][2][3][4] or the degree distribution [5][6][7]. They use these modifications to describe the diminished network at each stage of the cascade.…”

mentioning

confidence: 99%

Cascading failures in networks with proximate dependent nodes

et al. 2014

View full text Add to dashboard Cite

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a non-trivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases.Previous studies of the robustness of interdependent networks have focused on networks in which there is no constraint on the distance between the interdependent nodes [1][2][3][4][5][6][7][8][9]. However, many dependency links in the real world connect nearby nodes. For example, the international network of seaports and the network of national highways form a complex system. As seen recently from the effects of Hurricane Sandy in New York City, if a seaport is damaged, the city that depends on it will become isolated from the highway network due to the lack of fuel. Similarly, a city without roads cannot supply a seaport properly. However, a city will depend on a nearby seaport, not on one across the world. Li et. al [10] investigated distance-limited interdependent lattice networks by computer simulations and found that allowing only local interdependency links changed the resilience properties of the system. Here, we study the analytically tractable random networks. We study the mutual percolation of two interdependent random regular (RR) graphs. We build two identical networks, A and B, each of whose nodes are labeled 1...N . Each node is randomly connected by edges to exactly k other nodes, in such a way that the two networks have identical topologies. We then create one-to-one bidirectional dependency links, requiring that the shortest path between the interdependent nodes does not exceed an integer constant ℓ. Formally, we establish two isomorphisms between networks A and B, a topological isomorphism and a dependency isomorphism. The topological isomorphism is defined for each node A i as T (A i ) = B i and T (B i ) = A i . If Following the mutual percolation model described in Buldyrev et al.[1], we destroy a fraction (1 − p) of randomly selected nodes in A. Any nodes that, as a result, lost their connectivity links to the largest cluster (as defined in classical, single-network percolation theory [11,12]) are also destroyed. In the next stage, nodes in B that have their interdependent nodes in the other network destroyed are also destroyed. Consequently, the nodes that are isolated from the largest cluster in B as a result of the destruction of nodes in B are also destroyed. The iteration of this process, which alternates between the two networks, leads to a cascade of failures. The cascade ends when no more nodes fail in either network. The pair of remaining largest interdependent clusters in both networks is called a largest mutual componen...

show abstract