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

Equally important are the linkages which the models provide between theories at varying levels of abstraction, linkages which could be only briefly alluded to in this paper.38 The models allow one to trace the connection between specific human groupings and the place they occupy in more general sociological theory, whether that place is formal organizational theory, on the one hand, or urban and rural sociology on the other. Finally, with the qualitative differences indicated here, an opening wedge is provided for clarifying one of the knottier problems in community theory: the distinction between community and non-community. The implication is strong that the distinction is between systems designed to attain specific goals and those which have no such purposes, whose goals are at best diffuse.39

https://www.jstor.org/stable/pdfplus/2089916.pdf

Locating Leaders in Local Communities: A Comparison of Some Alternative Approaches

The implications of social structure for dominance hierarchies in red deer, Cervus elaphus L

Spheres, cubes and boxes: Graph dimensionality and network structure

Cette etude examine certaines consequences des idees de S. Nadel (1957) concernant les relations de role et les comportements specifiques. Les AA. ont analyse des donnees d'enquetes conduites dans les pays suivants : Autriche, Australie, Chine, Grande-Bretagne, Hongrie, Italie, Pays-Bas, Etats-Unis et Allemagne de l'Ouest. Les comportements specifiques liant certains des sujets furent determines a partir des reponses des sujets a six questions concernant diverses interactions entre ces sujets et d'autres individus. Apres quoi, on placa chacun de ces autres individus dans l'une des neuf categories possibles de relations de role. On calcula l'ajustement proportionnel iteratif des matrices de donnees, et les valeurs singulieres des matrices furent evaluees, permettant un examen des modeles de couples comportement-comportement, role-role et comportement-role. On observa une ressemblance remarquable des modeles pour les pays etudies, a la seule exception de la Chine, pour laquelle les reponses obtenues furent tres differentes

https://www.jstor.org/stable/pdfplus/27889502.pdf

Linton C. Freeman

Papers

Locating Leaders in Local Communities: A Comparison of Some Alternative Approaches

The implications of social structure for dominance hierarchies in red deer, Cervus elaphus L

Spheres, cubes and boxes: Graph dimensionality and network structure

An international comparative study of interpersonal behavior and role relationships

Estimating acquaintanceship volume