Eradicating catastrophic collapse in interdependent networks via reinforced nodes

Abstract

In interdependent networks, it is usually assumed, based on percolation theory, that nodes become nonfunctional if they lose connection to the network giant component. However, in reality, some nodes, equipped with alternative resources, together with their connected neighbors can still be functioning after disconnected from the giant component. Here, we propose and study a generalized percolation model that introduces a fraction of reinforced nodes in the interdependent networks that can function and support their neighborhood. We analyze, both analytically and via simulations, the order parameter-the functioning component-comprising both the giant component and smaller components that include at least one reinforced node. Remarkably, it is found that, for interdependent networks, we need to reinforce only a small fraction of nodes to prevent abrupt catastrophic collapses. Moreover, we find that the universal upper bound of this fraction is 0.1756 for two interdependent Erdős-Rényi (ER) networks: regular random (RR) networks and scale-free (SF) networks with large average degrees. We also generalize our theory to interdependent networks of networks (NONs). These findings might yield insight for designing resilient interdependent infrastructure networks.

Heterogeneous behavioral adoption in multiplex networks

“…If equation (23) is tangent to equation (24) when θ A < 1 and θ B < 1, there exists an discontinuous first-order phase transition [63]. At critical point, the following condition satisfies…”

Effective spreading from multiple leaders identified by percolation in the susceptible-infected-recovered (SIR) model

“…Our method is then devised in relation to the bond percolation model [15,[21][22][23][24] as follows. Given an undirected network G V E , ( )where V represents the set of nodes (i.e.…”

Asymmetry in interdependence makes a multilayer system more robust against cascading failures

“…To be concrete, we focus on a generic type of dynamical processes on multilayer networked systems: cascading failures that attest most relevantly to the robustness and resilience of the system. There is a large body of literature on cascading failures in single layer complex networks [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], and there have also been efforts in cascading dynamics in multilayer networks [4,[30][31][32][33][34]. The unique feature that distinguishes cascading dynamics in multilayer from those in single layer systems is that, in multilayer systems, failures can propagate from one network layer to another and trigger large-scale failures in an avalanche manner by the intricate strong node-to-node interaction pattern across the network layers.…”

“…While protecting the hub nodes can be an effective strategy to mitigate cascading failures in single layer networks, in interdependent systems this strategy is less effective [2,3]. Nonetheless, there are alternative methods to generate robust interdependent networks even in the strong dependence regime [31][32][33][34][35], where robustness can be enhanced with second-order phase transitions through mechanisms such as inter-similarity [36], geometric correlations [37,38], correlated community structures [39] and link overlaps [40,41]. In addition, it was found that the vulnerability of interdependent networked systems can be reduced through weakening the interlayer interaction [30].…”

“…A tacit assumption employed in most previous models of cascading failures in multilayer networks [4,[30][31][32][33][34] is that the layer interdependence will cause a node to fail completely should any of its neighboring nodes in the other layers become non-functional. For convenience, we regard such interdependence as "strong."…”