Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided

Network Analysis Methods for Modelling Tourism Inter- Organizational Systems

This chapter discusses the emerging network science approach to the study of complex adaptive systems and applies tools derived from statistical physics to the analysis of tourism destinations. The authors provide a brief history of network science and the characteristics of a network as well as different models such as small world and scale free networks, and dynamic properties such as resilience and information diffusion. The Italian resort island of Elba is used as a case study allowing comparison of the communication network of tourist organizations and the virtual network formed by the websites of these organizations. The study compares the parameters of these networks to networks from the literature and to randomly created networks. The analyses include computer simulations to assess the dynamic properties of these networks. The results indicate that the Elba tourism network has a low degree of collaboration between members. These findings provide a quantitative measure of network performance. In general, the application of network science to the study of social systems offers opportunities for better management of tourism destinations and complex social systems

Prediction and modelling of complex social networks and their evolution.

This thesis focuses on complex social networks in the context of computational approaches for their prediction and modelling. The increasing popularity and advancement of social net- works paired with the availability of social network data enable empirical analysis, inference, prediction and modelling of social patterns. This data-driven approach towards social science is continuously evolving and is crucial for modelling and understanding of human social behaviour including predicting future social interactions for a wide range of applications. The main difference between traditional datasets and network datasets is the presence of the relational components (links) between instances (nodes) of the network. These links and nodes induce intricate local and global patterns, defining the topology of a network. The topology is ever evolving, determining the dynamics of such a networked system. The work presented in this thesis starts with an extensive analysis of three standard network models, in terms of their properties and self-interactions as well as the size and density of the resultant graphs. These crucial analysis and understanding of the main network models are utilised to later develop a comprehensive network simulation framework. A set of novel nature-inspired link prediction approaches are then developed to predict the evolution of networks, based solely on their topologies. Building on top of these approaches, enhanced topological representations of networks are subsequently combined with node characteristics for the purpose of node classification. Finally, the proposed classification methods are extensively evaluated using simulated networks from our network simulation framework as well as two real-world citation networks. The link prediction approaches proposed in this research show that the topology of the network can be further exploited to improve the prediction of future relationships. Moreover, this research demonstrates the potential of blending state-of-the-art Machine Learning techniques with graph theory. To accelerate such advancements in the field of network science, this research also offers an open- source software to provide high-quality synthetic datasets

Structural property-aware multilayer network embedding for latent factor analysis

© 2017 Elsevier Ltd Multilayer network is a structure commonly used to describe and model the complex interaction between sets of entities/nodes. A three-layer example is the author-paper-word structure in which authors are linked by co-author relation, papers are linked by citation relation, and words are linked by semantic relation. Network embedding, which aims to project the nodes in the network into a relatively low-dimensional space for latent factor analysis, has recently emerged as an effective method for a variety of network-based tasks, such as collaborative filtering and link prediction. However, existing studies of network embedding both focus on the single-layer network and overlook the structural properties of the network, e.g., the degree distribution and communities, which are significant for node characterization, such as the preferences of users in a social network. In this paper, we propose four multilayer network embedding algorithms based on Nonnegative Matrix Factorization (NMF) with consideration given to four structural properties: whole network (NNMF), community (CNMF), degree distribution (DNMF), and max spanning tree (TNMF). Experiments on synthetic data show that the proposed algorithms are able to preserve the desired structural properties as designed. Experiments on real-world data show that multilayer network embedding improves the accuracy of document clustering and recommendation, and the four embedding algorithms corresponding to the four structural properties demonstrate the differences in performance on these two tasks. These results can be directly used in document clustering and recommendation systems

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples --- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Methods and Applications for Detecting Structure in Complex Networks.

The use of networks to represent systems of interacting components is now common in many fields including the biological, physical, and social sciences. Network models are widely applicable due to their relatively simple framework of vertices and edges. Network structure, patterns of connection between vertices, impacts both the functioning of networks and processes occurring on networks. However, many aspects of network structure are still poorly understood. This dissertation presents a set of network analysis methods and applications to real-world as well as simulated networks. The methods are divided into two main types: linear algebra formulations and probabilistic mixture model techniques. Network models lend themselves to compact mathematical representation as matrices, making linear algebra techniques useful probes of network structure. We present methods for the detection of two distinct, but related, network structural forms. First, we derive a measure of vertex similarity based upon network structure. The method builds on existing ideas concerning calculation of vertex similarity, but generalizes and extends the scope to large networks. Second, we address the detection of communities or modules in a specific class of networks, directed networks. We propose a method for detecting community structure in directed networks, which is an extension of a community detection method previously only known for undirected networks. Moving away from linear algebra formulations, we propose two methods for network structure detection based on probabilistic techniques. In the first method, we use the machinery of the expectation-maximization (EM) algorithm to probe patterns of connection among vertices in static networks. The technique allows for the detection of a broad range of types of structure in networks. The second method focuses on time evolving networks. We propose an application of the EM algorithm to evolving networks that can reveal significant structural divisions in a network over time.Ph.D.PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60774/1/eleicht_1.pd

Bayesian Networks and Gaussian Mixture Models in Multi-Dimensional Data Analysis with Application to Religion-Conflict Data

abstract: This thesis examines the application of statistical signal processing approaches to data arising from surveys intended to measure psychological and sociological phenomena underpinning human social dynamics. The use of signal processing methods for analysis of signals arising from measurement of social, biological, and other non-traditional phenomena has been an important and growing area of signal processing research over the past decade. Here, we explore the application of statistical modeling and signal processing concepts to data obtained from the Global Group Relations Project, specifically to understand and quantify the effects and interactions of social psychological factors related to intergroup conflicts. We use Bayesian networks to specify prospective models of conditional dependence. Bayesian networks are determined between social psychological factors and conflict variables, and modeled by directed acyclic graphs, while the significant interactions are modeled as conditional probabilities. Since the data are sparse and multi-dimensional, we regress Gaussian mixture models (GMMs) against the data to estimate the conditional probabilities of interest. The parameters of GMMs are estimated using the expectation-maximization (EM) algorithm. However, the EM algorithm may suffer from over-fitting problem due to the high dimensionality and limited observations entailed in this data set. Therefore, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are used for GMM order estimation. To assist intuitive understanding of the interactions of social variables and the intergroup conflicts, we introduce a color-based visualization scheme. In this scheme, the intensities of colors are proportional to the conditional probabilities observed.Dissertation/ThesisM.S. Electrical Engineering 201

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