The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

/pdf/introduction-to-social-network-methods-36g7099hce.pdf

Introduction to Social Network Methods

This chapter reviews social capital as discussed in the literature, identifies controversies and debates, considers some critical issues, and provides conceptual and research strategies for building a theory. It argues that such a theory and the research enterprise must be based on the fundamental understanding that social capital is captured from embedded resources in social networks. Such measurements can strength of tie network bridge, or intimacy, intensity, interaction and reciprocity be made relative to two frameworks: network resources and contact resources. There are many other measures, such as size, density, cohesion, and closeness of social networks which are candidates as measures for social capital. Network locations are necessary conditions of embedded resources. By considering social capital as assets in networks, the chapter discusses some issues in conceptualization, measurement, and causal mechanism. A proposed model identifies the exogenous factors leading to the acquisition (or the lack) of social capital as well as the expected returns of social capital.

Building a Network Theory of Social Capital

Social Network Analysis

Models of core/periphery structures

A Graph-theoretic perspective on centrality

Preface Introduction Mathematical Foundations Research Design Data Collection Data Management Multivariate Techniques Used in Network Analysis Visualization Testing Hypotheses Characterizing Whole Networks Centrality Subgroups Equivalence Analyzing Two-Mode Data Large Networks Ego Networks

Analyzing Social Networks

https://www.bebr.ufl.edu/sites/default/files/Borgatti%20and%20Everett%20-%201997%20-%20Network%20analysis%20of%202-mode%20data.pdf

Network analysis of 2-mode data

http://www.analytictech.com/borgatti/papers/egobet.pdf

Martin G. Everett

Papers

Models of core/periphery structures

A Graph-theoretic perspective on centrality

Analyzing Social Networks

Network analysis of 2-mode data

Ego network betweenness