Ranking in evolving complex networks

Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Many popular ranking algorithms (such as Google’s PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. At the same time, recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of network traffic, prediction of future links, and identification of significant nodes

Diffusion and Supercritical Spreading Processes on Complex Networks

Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen. Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden. In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind. Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese. Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist. Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent. In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues. In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks. We study three different problems related to spreading processes in the supercritical regime. First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility. The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns. Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how close a node is, on average, to the other nodes. These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field

Robust interventions in network epidemiology

Which individual should we vaccinate to minimize the spread of a disease? Designing optimal interventions of this kind can be formalized as an optimization problem on networks, in which we have to select a budgeted number of dynamically important nodes to receive treatment that optimizes a dynamical outcome. Describing this optimization problem requires specifying the network, a model of the dynamics, and an objective for the outcome of the dynamics. In real-world contexts, these inputs are vulnerable to misspecification---the network and dynamics must be inferred from data, and the decision-maker must operationalize some (potentially abstract) goal into a mathematical objective function. Moreover, the tools to make reliable inferences---on the dynamical parameters, in particular---remain limited due to computational problems and issues of identifiability. Given these challenges, models thus remain more useful for building intuition than for designing actual interventions. This thesis seeks to elevate complex dynamical models from intuition-building tools to methods for the practical design of interventions. First, we circumvent the inference problem by searching for robust decisions that are insensitive to model misspecification.If these robust solutions work well across a broad range of structural and dynamic contexts, the issues associated with accurately specifying the problem inputs are largely moot. We explore the existence of these solutions across three facets of dynamic importance common in network epidemiology. Second, we introduce a method for analytically calculating the expected outcome of a spreading process under various interventions. Our method is based on message passing, a technique from statistical physics that has received attention in a variety of contexts, from epidemiology to statistical inference.We combine several facets of the message-passing literature for network epidemiology.Our method allows us to test general probabilistic, temporal intervention strategies (such as seeding or vaccination). Furthermore, the method works on arbitrary networks without requiring the network to be locally tree-like .This method has the potential to improve our ability to discriminate between possible intervention outcomes. Overall, our work builds intuition about the decision landscape of designing interventions in spreading dynamics. This work also suggests a way forward for probing the decision-making landscape of other intervention contexts. More broadly, we provide a framework for exploring the boundaries of designing robust interventions with complex systems modeling tools