Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Maximising Influence in Non-blocking Cascades of Interacting Concepts

Abstract. In large populations of autonomous individuals, the propa-gation of ideas, strategies or infections is determined by the composite effect of interactions between individuals. The propagation of concepts in a population is a form of influence spread and can be modelled as a cascade from a set of initial individuals through the population. Un-derstanding influence spread and information cascades has many appli-cations, from informing epidemic control and viral marketing strategies to understanding the emergence of conventions in multi-agent systems. Existing work on influence spread has mainly considered single concepts, or small numbers of blocking (exclusive) concepts. In this paper we focus on non-blocking cascades, and propose a new model for characterising concept interaction in an independent cascade. Furthermore, we propose two heuristics, Concept Aware Single Discount and Expected Infected, for identifying the individuals that will maximise the spread of a partic-ular concept, and show that in the non-blocking multi-concept setting our heuristics out-perform existing methods.

Towards designing robust coupled networks

Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of selecting a minimum number of autonomous nodes that guarantee a smooth transition in robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five compared to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy

The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

Avoiding catastrophic failure in correlated networks of networks

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.Comment: 40 pages, 7 figure

Multiplex PageRank

(15 pages, 6 figures

Default cascades in complex networks: Topology and systemic risk

The recent crisis has brought to the fore a crucial question that remains still open: what would be the optimal architecture of financial systems? We investigate the stability of several benchmark topologies in a simple default cascading dynamics in bank networks. We analyze the interplay of several crucial drivers, i.e. network topology, banks' capital ratios, market illiquidity, and random vs targeted shocks. We find that, in general, topology matters only – but substantially – when the market is illiquid. No single topology is always superior to others. In particular, scale-free networks can be both more robust and more fragile than homogeneous architectures. This finding has important policy implications. We also apply our methodology to a comprehensive dataset of an interbank market from 1999 to 2011.SCOPUS: ar.jinfo:eu-repo/semantics/publishe