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

Cliques, Galois lattices, and the structure of human social groups☆

Does the concept of societal complexity refer to a single dimension? Data have been gathered from a sample of forty-eight societies and scored according to Guttman's scalogram analysis. Six out of eight variables tested vary systematically and constitute an acceptable scale. This is empirical evidence for the relevance of societal complexity. The study demonstrates a technique for testing polar ideal types which allows the investigator to determine whether or not they are empirically based.

https://www.jstor.org/stable/pdfplus/2773238.pdf

Societal Complexity: An Empirical Test of a Typology of Societies

Tests for the indirect assessment of at t i tudes have gained some currency in the l i terature of social psychology. T h e y have been used pr imari ly as indexes to behavior in si tuations where social pressures have been assumed to inhibit truthful response to direct questions. In such si tuat ions investigators have frequently assumed that responses to indirect questions provide m o r e valid behavioral indexes than responses to direct questions. A few studies of the correlation between direct and indirect questions have been made (Campbell , 1953 ; Pa r i sh & Campbell, 1953 ; P roshansky , 1 9 4 3 ; Rank in & Campbell, 1955; Robinson & Rohde, 1946 ; and Sanford & Rosenstock, 1952) , but a l though Campbell has questioned the v a l i i t y of indirect questions as indexes to behavior, no systematic s tudy of this question has been reported. T h e present study was designed in an attempt to examine the validity of several types of indirect questions and a direct question against the cri terion of overt behavior.

Invalidity of indirect and direct measures of attitude toward cheating

This is a study of a collection of social scientists. It examines the social context out of which they develop close friendship ties and the impact of an extended computer conference on such ties. The perspective of R. H. Atkin (1974) is used to uncover shifts in the structure of ties among the participants.

/pdf/q-analysis-and-the-structure-of-friendship-networks-58pjne451y.pdf

Q-analysis and the structure of friendship networks

We explore how humans solve some problems of living in a social world. In particular, we focus on the ability to see affiliation or alliance patterns in social communities. We draw on data from two naturalistic studies in which subjects were observed interacting and required to reveal their perceptions of the patterning of that interaction. In both cases, the observed interaction patterns and the subjects' reports correspond closely. But in both cases, subjects are shown to simplify and exaggerate the observed patterning. Individual subjects, moreover, appear able to reveal more details about interaction patterns among those with whom they interact frequently, while they gloss over details involving interaction among others with whom their own interaction is infrequent.

Linton C. Freeman

Papers

Cliques, Galois lattices, and the structure of human social groups☆

Societal Complexity: An Empirical Test of a Typology of Societies

Invalidity of indirect and direct measures of attitude toward cheating

Q-analysis and the structure of friendship networks

Interpersonal Proximity in Social and Cognitive Space