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Example adjacency matrices for networks with 60 nodes in 2 or 3 roles and corresponding image graphs. Rows and columns in matrices are ordered such that nodes of the same type (in the same role) are adjacent. Hence, blocks appear in the adjacency matrix due to the similar pattern of connectivity among nodes of the same type. The types are represented by a single node in the image graph. Background shading of matrices reﬂects the link density in blocks. We show only those three-role models which are not isomorphic and which cannot be reduced to a block model of two roles only.
Identifying communities within energy landscapes. Physical Review E, 71:046101, 2005. 26 51. S. D. P. Vecchi. Optimization by simulated annealing. Science, 220:671–680, 1983. 26 52. J. Duch and A. Arenas. Community detection in complex networks using extremal optimization. Physical Review E, 72:027104, 2005. 1 Mapping the Problem Common to all of the before-mentioned approaches is their attempt to discover patterns in the link structure of networks. Patterns were either block structures in the adjacency matrix or – more speciﬁcally – cohesive subgroups.
Regular equivalence: general theory. The Journal of Mathematical Sociology, 19:29–52, 1994. 13 15. P. Doreian, V. Batagelj, and A. Ferligoj. Generalized Blockmodeling. Cambridge University Press, New York, 2005. 15, 16 16. M. Mcperson, L. Smith-Lovin, and J. M. Cook. Birds of a feather: Homophily in social networks. Annual Review of Sociology, 27:415:44, 2001. 18 17. M. Girvan and M. E. J. Newman. Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America, 99(12):7821–7826, 2002.