Towards designing robust coupled networks

Schneider, Christian; Yazdani, Nasser; Araújo, Nuno A. M.; Havlin, Shlomo; Herrmann, Hans J.

doi:10.1038/srep01969

Cited by 181 publications

(131 citation statements)

References 28 publications

(40 reference statements)

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“…[12], for homogeneous networks, the robustness of the networks increases with α due to the fact that the higher degree nodes of both networks, that are the ones that sustain the functionality of the networks, are autonomous. Our theoretical equations allow to find a surprising behavior of the transitions with two critical thresholds at p = p (1) and (3) with the condition det(…”

Section: Theoretical Resultsmentioning

confidence: 99%

A triple point induced by targeted autonomization on interdependent scale-free networks

Valdez¹,

Macri²,

Braunstein³

2014

J. Phys. A: Math. Theor.

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Recent studies have shown that in interdependent networks an initial failure of a fraction 1 − p of nodes in one network, exposes the system to cascade of failures. Therefore it is important to develop efficient strategies to avoid their collapse. Here, we provide an exact theoretical approach to study the evolution of the cascade of failures on interdependent networks when a fraction α of the nodes with higher connectivity are autonomous. We found, for a pair of heterogeneous networks, two critical percolation thresholds that depend on α, separating three regimes with very different network's final sizes that converge into a triple point in the plane p − α. Our findings suggest that the heterogeneity of the networks represented by high degree nodes is the responsible of the rich phase diagrams found in this and other investigations.

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Section: Theoretical Resultsmentioning

confidence: 99%

A triple point induced by targeted autonomization on interdependent scale-free networks

Valdez¹,

Macri²,

Braunstein³

2014

J. Phys. A: Math. Theor.

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“…The error and attack tolerance of a network under structural disturbance has been one of the major problems in network theory [26][27][28], which has also been addressed in the context of interdependent networks [10,21,36,37] in recent years. In this section, we consider this problem for multiplex networks with interlayer degree correlations.…”

Section: Error and Attack Tolerancementioning

confidence: 99%

Network robustness of multiplex networks with interlayer degree correlations

et al. 2014

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We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address various notions of the network robustness relevant to multiplex networks such as the resilience of ordinary-and mutual connectivity under random or targeted node removals as well as the biconnectivity. We found that correlated coupling can affect the structural robustness of multiplex networks in diverse fashion. For example, for maximallycorrelated duplex networks, all pairs of nodes in the giant component are connected via at least two independent paths and network structure is highly resilient to random failure. In contrast, anticorrelated duplex networks are on one hand robust against targeted attack on high-degree nodes, but on the other hand they can be vulnerable to random failure.

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“…from different geographical regions and this information is required by the power stations that supply electricity to those regions. This setting has been investigated from different perspectives over the past few years [1], [4], [5], [15], [25]- [27] and our results add to this literature by studying the game-theoretic allocation of interconnecting edges between the power and sensor networks. We model dependencies between the substations and sensors (which correspond to nodes in G 1 and G 2 , respectively) by the network G I .…”

Section: Introductionmentioning

confidence: 81%

“…Examples include coupled energy infrastructure and communication networks [4], cyberphysical systems [5], and transportation networks (such as the flight networks of different airlines) [6]. Understanding the structure of large-scale networks and the implications of this structure for the effective functioning of the network has been the subject of many studies throughout the past decade [7], [8].…”

Section: Introductionmentioning

confidence: 99%

“…One approach to investigate this problem is through the framework of random graphs where each subnetwork is drawn from a certain probability distribution [9], [10]. For (single) random networks, properties such as connectivity, robustness against structural and dynamical failures, and edge expansion have been widely investigated in the literature [11]- [14], with recent extensions to interconnected networks [4], [15]- [18].…”

Section: Introductionmentioning

confidence: 99%

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The Game-Theoretic Formation of Interconnections Between Networks

Shahrivar

Sundaram

2017

IEEE J. Select. Areas Commun.

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We introduce a network design game where the objective of the players is to design the interconnections between the nodes of two different networks G 1 and G 2 in order to maximize certain local utility functions. In this setting, each player is associated with a node in G 1 and has functional dependencies on certain nodes in G 2 . We use a distance-based utility for the players in which the goal of each player is to purchase a set of edges (incident to its associated node) such that the sum of the distances between its associated node and the nodes it depends on in G 2 is minimized. We consider a heterogeneous set of players (i.e., players have their own costs and benefits for constructing edges). We show that finding a best response of a player in this game is NP-hard. Despite this, we characterize some properties of the best response actions which are helpful in determining a Nash equilibrium for certain instances of this game. In particular, we prove existence of pure Nash equilibria in this game when G 2 contains a star subgraph, and provide an algorithm that outputs such an equilibrium for any set of players. Finally, we show that the price of anarchy in this game can be arbitrarily large.

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Towards designing robust coupled networks

Cited by 181 publications

References 28 publications

A triple point induced by targeted autonomization on interdependent scale-free networks

A triple point induced by targeted autonomization on interdependent scale-free networks

Network robustness of multiplex networks with interlayer degree correlations

The Game-Theoretic Formation of Interconnections Between Networks

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