Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Interacting Spreading Processes in Multilayer Networks: A Systematic Review

© 2013 IEEE. The world of network science is fascinating and filled with complex phenomena that we aspire to understand. One of them is the dynamics of spreading processes over complex networked structures. Building the knowledge-base in the field where we can face more than one spreading process propagating over a network that has more than one layer is a challenging task, as the complexity comes both from the environment in which the spread happens and from characteristics and interplay of spreads' propagation. As this cross-disciplinary field bringing together computer science, network science, biology and physics has rapidly grown over the last decade, there is a need to comprehensively review the current state-of-the-art and offer to the research community a roadmap that helps to organise the future research in this area. Thus, this survey is a first attempt to present the current landscape of the multi-processes spread over multilayer networks and to suggest the potential ways forward

Protection against Contagion in Complex Networks

In real-world complex networks, harmful spreads, commonly known as contagions, are common and can potentially lead to catastrophic events if uncontrolled. Some examples include pandemics, network attacks on crucial infrastructure systems, and the propagation of misinformation or radical ideas. Thus, it is critical to study the protective measures that inhibit or eliminate contagion in these networks. This is known as the network protection problem. The network protection problem investigates the most efficient graph manipulations (e.g., node and/or edge removal or addition) to protect a certain set of nodes known as critical nodes. There are two types of critical nodes: (1) predefined, based on their importance to the functionality of the network; (2) unknown, whose importance depends on their location in the network structure. For both of these groups and with no assumption on the contagion dynamics, I address three major shortcomings in the current network protection research: namely, scalability, imprecise evaluation metric, and assumption on global graph knowledge. First, to address the scalability issue, I show that local community information affects contagion paths through characteristic path length. The relationship between the two suggests that, instead of global network manipulations, we can disrupt the contagion paths by manipulating the local community of critical nodes. Next, I study network protection of predefined critical nodes against targeted contagion attacks with access to partial network information only. I propose the CoVerD protection algorithm that is fast and successfully increases the attacker’s effort for reaching the target nodes by 3 to 10 times compared to the next best-performing benchmark. Finally, I study the more sophisticated problem of protecting unknown critical nodes in the context of biological contagions, with partial and no knowledge of network structure. In the presence of partial network information, I show that strategies based on immediate neighborhood information give the best trade-off between performance and cost. In the presence of no network information, I propose a dynamic algorithm, ComMit, that works within a limited budget and enforces bursts of short-term restriction on small communities instead of long-term isolation of unaffected individuals. In comparison to baselines, ComMit reduces the peak of infection by 73% and shortens the duration of infection by 90%, even for persistent spreads

Modelling the social dynamics of contagion and discovery using dynamical processes on complex networks.

PhD Thesis.Complex networks have been successfully used to describe the social structure on top of which many real-world social processes take place. In this thesis, I focus on the development of network models that aim at capturing the fundamental mechanisms behind the dynamics of adoption of ideas, behaviours, or items. I start considering the transmission of a single idea from one individual to another, in an epidemic-like fashion. Recent evidence has shown that mechanisms of complex contagion can effectively capture the fundamental rules of social reinforcement and peer pressure proper of social systems. Along this line, I propose a model of complex recovery in which the social influence mechanism acts on the recovery rule rather than on the infection one, leading to explosive behaviours. Yet, in human communication, interactions can occur in groups. I thus expand the pairwise representation given by graphs using simplicial complexes instead. I develop a model of simplicial contagion, showing how the inclusion of these higher-order interactions can dramatically alter the spreading dynamics. I then consider an individual and model the dynamics of discovery as paths of sequential adoptions, with the first visit of an idea representing a novelty. Starting from the empirically observed dynamics of correlated novelties, according to which one discovery leads to another, I develop a model of biased random walks in which the exploration of the interlinked space of possible discoveries has the byproduct of influencing also the strengths of their connections. Balancing exploration and exploitation, the model reproduces the basic footprints of real-world innovation processes. Nevertheless, people do not live and work in isolation, and social ties can shape their behaviours. Thus, I consider interacting discovery processes to investigate how social interactions contribute to the collective emergence of new ideas and teamwork, and explorers can exploit opportunities coming from their social contacts

Complex Quantum Contagion: A Quantum-Like Approach for The Analysis of Co-Evolutionary Dynamics of Social Contagion

Modeling the dynamics of social contagion processes has recently attracted a substantial amount of interest from researchers due to its wide applicability in network science, multi-agent systems, information science, and marketing. Unlike in biological spreading, the existence of a reinforcement effect in social contagion necessitates considering the complexity of individuals in the systems. Although many studies acknowledged the heterogeneity of the individuals in their adoption of information (or behavior), there are no studies that take into account the individuals\u27 uncertainty during their decision-making despite its theoretical and experimental evidence in behavioral economics, decision science, cognitive science, or multi-agent systems. This resulted in less than optimal modeling of social contagion dynamics in the existence of phase transition in the final adoption size versus transmission probability. We believe that it is mainly because traditional approaches do not consider the uncertainty stemming from agent interactions through an information exchange that can influence individuals\u27 emotions, change subconscious feelings, and trigger subjective biases. To address this problem, we propose quantum-like generalization of social contagion analysis for the analysis of co-evolutionary dynamics of social contagion. For this purpose, we employed Inverse Born Problem (IBP) to represent probabilistic entities as complex probability amplitudes in edge-based compartmental theory and demonstrated that our novel approach performs better in the prediction of social contagion dynamics through extensive simulations on random regular networks