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.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

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.

/pdf/community-structure-in-social-and-biological-networks-1jamu4rcfv.pdf

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

Social Networks and the Structure Experiment

This note extends and elaborates Hubert's attempt to provide an interpretation of Freeman's measure of association,ϑ. Theϑ measure is used in a a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution ofϑ.

A further note on freeman's measure of association

From time to time a branch of science captures the imagination of the public; it gets "hot." When that happens, references to the "hot" item appear in newspapers, in novels, in movies -even in cartoons. Forty odd years ago, for example, Ray Birdwhistell (1952) first introduced kinesics, the field concerned with the importance of non-verbal gestures in human communication. Very soon, Al Capp introduced a new character in his comic strip, Li'l Abner. Capp began a series of based on the activities of a "Professor Fleasong," a specialist in the study of "toe gestures."

/pdf/see-you-in-the-funny-papers-cartoons-and-social-networks-atz37nzul2.pdf

Linton C. Freeman

Papers

Social Networks and the Structure Experiment

A further note on freeman's measure of association

See you in the Funny Papers: Cartoons and Social Networks

The Changing Functions of a Folksong

Rethinking the Role Concept: Homomorphisms on Social Networks