Presented in a comprehensive manner, this book provides a comprehensive foundation in algebraic approaches for the analysis of different types of social networks such as multiple, signed, and affiliation networks. The study of such configurations corresponds to the structural analysis within the social sciences, and the methods applied for the analysis are in the areas of abstract algebra, combinatorics, and graph theory. Current research in social networks has moved toward the examination of more realistic but also more complex social relations by which agents or actors are connected in multiple ways. Addressing this trend, this book offers hands-on training of the algebraic procedures presented along with the computer package multiplex, written by the book’s author specifically to perform analyses of multiple social networks. An introductory section on both complex networks and for R will feature, however the subjects themselves correspond to advanced courses on social network analysis with the specialization on algebraic models and methods.

The book should be of interest to all researchers interested in using social network methods.

Network algebra considers the algebraic study of networks and their behavior. It approaches the models in a sharp and simple manner. This book takes an integrated view of a broad range of applications, varying from concrete hardware-oriented models to high-level software-oriented models.

Focused on the mathematical foundations of social media analysis, Graph-Based Social Media Analysis provides a comprehensive introduction to the use of graph analysis in the study of social and digital media. It addresses an important scientific and technological challenge, namely the confluence of graph analysis and network theory with linear alge

Since the publication of Herbert Spencer's Principles of Sociology in 1875, the use of social structure as a defining concept has produced a large body of creative speculations, insights, and intuitions about social life. However, writers in this tradition do not always provide the sorts of formal definitons and propositions that are the building blocks of modern social research. In its broad-ranging examination of the kind of data that form the basis for the systematic study of social structure, Research Methods in Social Network Analysis marks a significant methodological advance in network studies. As used in this volume, social structure refers to a bundle of intuitive natural language ideas and concepts about patterning in social relationships among people. In contrast, social networks is used to refer to a collection of precise analytic and methodological concepts and procedures that facilitate the collection of data and the systematic study of such patterning. Accordingly, the book's five sections are arranged to address analytical problems in a series of logically ordered stages or processes. The major contributors define the fundamental modes by which social structural phenomena are to be represented; how boundaries to a social structure are set; how the relations of a network are measured in terms of structure and content; the ways in which the relational structure of a network affects system actors; and how actors within a social network are clustered into cliques or groups. The chapters in the last section build on solutions to problems proposed in the previous sections. This highly unified approach to research design combined with a representative diversity of viewpoints makes Research Methods in Social Network Analysis a state-of-the-art volume.

This sparkling Handbook offers an unrivalled resource for those engaged in the cutting edge field of social network analysis. Systematically, it introduces readers to the key concepts, substantive topics, central methods and prime debates. Among the specific areas covered are: Network theory Interdisciplinary applications Online networks Corporate networks Lobbying networks Deviant networks Measuring devices Key Methodologies Software applications. The result is a peerless resource for teachers and students which offers a critical survey of the origins, basic issues and major debates. The Handbook provides a one-stop guide that will be used by readers for decades to come.

Ideas about social structure and social networks are very old. People have always believed that biological and social links among individuals are important. But it wasn't until the early 1930s that systematic research that explored the patterning of social ties linking individuals emerged. And it emerged, not once, but several times in several different social science fields and in several places. This book reviews these developments and explores the social processes that wove all these "schools" of network analysis together into a single coherent approach.

Models and Methods in Social Network Analysis presents the most important developments in quantitative models and methods for analyzing social network data that have appeared during the 1990s. Intended as a complement to Wasserman and Faust's Social Network Analysis: Methods and Applications, it is a collection of articles by leading methodologists reviewing advances in their particular areas of network methods. Reviewed are advances in network measurement, network sampling, the analysis of centrality, positional analysis or blockmodelling, the analysis of diffusion through networks, the analysis of affiliation or 'two-mode' networks, the theory of random graphs, dependence graphs, exponential families of random graphs, the analysis of longitudinal network data, graphical techniques for exploring network data, and software for the analysis of social networks.

Pioneering introduction of unprecedented breadth and scope to inferential and statistical methods for network analysis.

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology. DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes. The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective. The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.