Multilayer and Interconnected Networks: Applications (MINA)  (MINA) Session 1

Abstract: A framework for studying the vulnerability and the recovery of networks of interdependent networks will be presented.In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This is also the case when some nodes like certain locations play a role in two networks --multiplex. This may happen recursively and can lead to a cascade of failures and to a sudden fragmentation of the system.I will present analytical solutions for the critical thresholds and the giant component of a network of n interdependent networks.I will show, that the general theory has many novel features that are not present in the classical network theory. When recovery of components is possible global spontaneous recovery of the networks and hysteresis phenomena occur and the theory suggests an optimal repairing strategy for a system of systems.I will also show that interdependent networks embedded in space are significantly more vulnerable compared to non embedded networks. In particular, small localized attacks of zero fraction may lead to cascading failures and catastrophic consequences.Thus, analyzing real data and realistic models of network of networks is highly required to understand the system vulnerability. Close

Abstract: In this talk we study the impact that mobility patterns have on the onset of epidemics when different classes of individuals coexist within a metapopulation. Each class of individuals show different mobility patterns between the patches composing the metapopulation. Thus, the presence of M different types of individuals turns the usual networked metapopulation into a multiplex metapopulation of M layers, where each layer encodes the mobility network of each type of individuals. We will develop a Markovian formulation for calculating the time evolution of the infected individuals in each patch and compare our model with MonteCarlo agent based simulations. In addition, we focus on two particular datasets from the cities of Medell?n and Bogot?, both in Colombia. Although mobility patterns in these two cities are similar from those typically found for large cities, these datasets provide additional information about the socioeconomic status of the individuals. This information is particularly important when the level of inequality in a society is large, as it is the case in Colombia. Thus, taking advantage of this additional information we will analyze how the different mobility pattern of each socioeconomic class affect the onset of epidemics. Close

Abstract: Understanding the evolution of cooperation is one of the most fascinating challenges in many disciplines. There is a large amount of literature analysing the mechanisms for cooperation to emerge and to be sustained, both from theoretical and experimental studies. Another way to understand the evolution of cooperation in human societies consist in deciphering the cooperative behaviour in ancient communities from historical records. In a previous work we studied cooperation in the Yamana society that inhabited Argentina and observed that the emergence of an informal network of vigilance promoted cooperation. Several field studies have found evidence of humans exposing a pro-social behaviour when being observed by others and also under the presence of subtle cues of being watched. The observability effect (the increase of cooperation under vigilance) seems to be driven by our reputational concerns, bringing the indirect reciprocity mechanism into play. This work explores the effect of vigilance on cooperation in networked systems, in the framework of the Prisoners? Dilemma game. We study the bidirectionally-coupled vigilance and game dynamics. We quantify the impact of the topological structure of the network, and the interplay between vigilance and behaviour, on the outcome of cooperation. Moreover, we study the impact of vigilance on cooperation when the individuals have to afford a cost to become vigilant actors. We also analyse the influence of network multiplexity, i.e. the interconnection of different topological structures for the vigilance and the game networks, and the impact of layer-degree correlations, i.e. when node degrees of the multiplex layers are not randomly distributed but correlated. Our results show that vigilant actors can significantly affect the levels of cooperation, not only by enhancing cooperation in regions of the phase diagram where cooperation is expected to hold, but also by altering the critical point for the emergence of cooperation. Close

Abstract: Recent studies of multimodal urban transportation networks have used the framework of multiplex network analysis to illuminate their structure and make analytic or simulation-based inferences about their dynamics. However, these systems are intrinsically sociotechnical, and their dynamical behavior depends not only on structure, but also on user behavior--particularly travel demand. We present the first study of an urban transportation system combining multiplex network analysis and validated Origin-Destination travel demand, using Riyadh's planned metro as a case study. First, we develop methods for analyzing the impact of additional transportation layers on existing dynamics, and show that the structure of demand plays a key role in determining qualitative system behavior. We then demonstrate the existence of fundamental limits to changes in traffic dynamics due to the intrinsic geometry of the metro layer. Finally, we develop a simple analytical framework for informing the planning of additional feeder layers (such as buses) to maximize the impact of the metro on global congestion. The techniques we present are computationally practical, easily extensible to arbitrary numbers of transportation layers, and implemented in open-source software. Close

Abstract: In multi-layer networks with directed links, introducing measures of dependency between different layers requires more than a straightforward extension of the multiplexity measures that have been developed for undirected multiplexes. In particular, one should take into account the effects of reciprocity, i.e. the tendency of pairs of vertices to establish mutual connections. In single-layer networks, reciprocity is a crucial structural property affecting several dynamical processes. Here we extend it to multiplexes and introduce the notion of multireciprocity, defined as the tendency of links in one layer to be reciprocated by links in a different layer. While ordinary reciprocity reduces to a scalar quantity, multireciprocity requires a square matrix generated by all the possible pairs of layers. We introduce multireciprocity metrics valid for both binary and weighted multiplexes and provide an empirical analysis of the World Trade Multiplex, representing the import-export relationships between world countries in different products. We show that several pairs of layers exhibit strong multiplexity, an effect which is however largely encoded into the degree or strength sequences of individual layers. We also find that most pairs of commodities are characterised by positive multireciprocity, and that such values are significantly lower than the usual reciprocity measured on the aggregated network. Moreover, layers with low (high) internal reciprocity are embedded within groups of layers with low (high) mutual multireciprocity. We finally identify robust empirical patterns showing that joint multi-layer connection probabilities can be reconstructed from marginal ones via the multireciprocity matrix. Therefore the latter can bridge the gap between single-layer properties and truly multiplex information. Close

Abstract: Focusing on the dynamics of multiplex networks, we discuss some examples where multiplexity gives rise to the emergence of novel dynamical behaviors, otherwise unobserved in the dynamics of single-layer networks. Close