Social Networks with Rich Edge Semantics

Description

Social Networks with Rich Edge Semantics introduces a new mechanism for representing social networks in which pairwise relationships can be drawn from a range of realistic possibilities, including different types of relationships, different strengths in the directions of a pair, positive and negative relationships, and relationships whose intensities change with time. For each possibility, the book shows how to model the social network using spectral embedding. It also shows how to compose the techniques so that multiple edge semantics can be modeled together, and the modeling techniques are then applied to a range of datasets. Features Introduces the reader to difficulties with current social network analysis, and the need for richer representations of relationships among nodes, including accounting for intensity, direction, type, positive/negative, and changing intensities over time Presents a novel mechanism to allow social networks with qualitatively different kinds of relationships to be described and analyzed Includes extensions to the important technique of spectral embedding, shows that they are mathematically well motivated and proves that their results are appropriate Shows how to exploit embeddings to understand structures within social networks, including subgroups, positional significance, link or edge prediction, consistency of role in different contexts, and net flow of properties through a node Illustrates the use of the approach for real-world problems for online social networks, criminal and drug smuggling networks, and networks where the nodes are themselves groups Suitable for researchers and students in social network research, data science, statistical learning, and related areas, this book will help to provide a deeper understanding of real-world social networks. Content: IntroductionWhat is a social network?The multiple aspects of relationshipsFormally representing social networksThe core model Representing networks to understand their structures Building layered models BackgroundGraph Theory Background Spectral graph theory The spectral pipeline Spectral approaches to clustering Modelling relationships of different types Typed edge model approachTyped edge spectral embedding Applications of typed networksModelling asymmetric relationships Conventional directed spectral graph embedding Directed edge layered approach Applications of directed networks Modelling asymmetric relationships with multiple types Combining directed and typed embeddings Layered approach and compositions Applying directed typed embeddings Modelling relationships that change over time Temporal networks Applications of temporal networks Modelling positive and negative relationships The signed LaplacianUnnormalized spectral Laplacians of signed graphs Normalized spectral Laplacians of signed graphs Applications of signed networks Signed graph-based semi-supervised learning Approach The problems of imbalance in graph data Combining directed and signed embeddings Composition of directed and signed layer modelsApplication to signed directed networks Extensions to other compositions Appendices RatioCut consistency with two versions of each node Ncut consistency with multiple versions of each node Signed unnormalized clustering Signed normalized Laplacian Lsns clustering Signed normalized Laplacian Lbns clustering Example Matlab functions to implement spectral embeddings