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Role models for complex networks
Institute for Theoretical Physics, University of Würzburg, 97074 Würzburg, Germany
2 Department of Anthropology, Institute of Mathematical Behavioral Sciences, School of Social Sciences, University of California, Irvine, CA, 92697, USA
Corresponding author: a firstname.lastname@example.org
Published online: 8 December 2007
We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.75.Hc – Networks and genealogical trees / 89.65.Gh – Economics; econophysics, financial markets, business and management / 89.65.Ef – Social organizations; anthropology
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007