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.
Table of Contents
Introduction
What is a social network?
The multiple aspects of relationships
Formally representing social networks
The core model
Representing networks to understand their structures
Building layered models
Background
Graph Theory Background
Spectral graph theory
The spectral pipeline
Spectral approaches to clustering
Modelling relationships of different types
Typed edge model approach
Typed edge spectral embedding
Applications of typed networks
Modelling 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 Laplacian
Unnormalized 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 models
Application 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
