Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

https://www.bebr.ufl.edu/sites/default/files/Centrality%20in%20Social%20Networks.pdf

Centrality in social networks conceptual clarification

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

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Community structure in social and biological networks

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

/pdf/finding-and-evaluating-community-structure-in-networks-1o9f6y8pyr.pdf

Finding and evaluating community structure in networks.

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

Cognitive Structure and Informant Accuracy

Centrality in social networks: ii. experimental results☆

Based on a conference held in Laguna Beach, CA, 1980. Comprises 14 essays on network representations and boundaries, relational structure, clustering and positioning of actors. No index. Annotation copyright Book News, Inc. Portland, Or.

Research Methods in Social Network Analysis

Two models of the structural form of small, informal groups are compared. One, derived by Winship, requires that patterns of social affiliation be strictly transitive. The other, based on Granovetter's ideas about weak and strong ties, requires only a special limited form of transitivity. When these alternative models are tested with data on human interaction, it turns out that the Winship model does not fit the data but that the model developed from Granovetter's work does.

The Sociological Concept of "Group": An Empirical Test of Two Models

This paper shows that people are aware of who is affiliated with whom in their immediate social world. Their perceptions of the patterning oh affiliation, however, do not correspond to the patterning actually displayed by interacting humans. Affiliation is not categorical; perceptions of affiliation are, however. On the basis of experimental evidence about errors in learning simple social structures, a theory that accounts for this discrepancy is proposed. This theory suggests that people impose a categorical form on noncategorical affiliation patterns by a process of filling in the blanks in their experience

Linton C. Freeman

Papers

Cognitive Structure and Informant Accuracy

Centrality in social networks: ii. experimental results☆

Research Methods in Social Network Analysis

The Sociological Concept of "Group": An Empirical Test of Two Models

Filling in the Blanks: A Theory of Cognitive Categories and the Structure of Social Affiliation