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Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity Q as… (More)

A fast community detection algorithm based on a q-state Potts model is presented. Communities (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the… (More)

It is widely believed that the modular organization of cellular function is reflected in a modular structure of molecular networks. A common view is that a "module" in a network is a cohesively linked group of nodes, densely connected internally and sparsely interacting with the rest of the network. Many algorithms try to identify functional modules in… (More)

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from… (More)

Inference of hidden classes in stochastic block model is a classical problem with important applications. Most commonly used methods for this problem involve na¨ıve mean field approaches or heuristic spectral methods. Recently, belief propagation was proposed for this problem. In this contribution we perform a comparative study between the three methods on… (More)

We study dynamical reversibility in stationary stochastic processes from an information-theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations. In particular, we examine stationary processes represented or generated by edge-emitting, finite-state… (More)

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade, the overabundance of certain subnetwork patterns, i.e., the so-called motifs, has attracted much attention. It has been hypothesized that these motifs, instead of links, serve as the building blocks of… (More)

SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work… (More)

—The mining of graphs in terms of their local sub-structure is a well-established methodology to analyze networks. It was hypothesized that motifs-subgraph patterns which appear significantly more often than expected at random-play a key role for the ability of a system to perform its task. Yet the framework commonly used for motif-detection averages over… (More)