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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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Factor graphs and graph ensembles

Factor graphs and graph ensembles

(p.173) 9 Factor graphs and graph ensembles
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

Probabilistic systems involving a large number of simple variables with mutual dependencies appear recurrently in several fields of science. It is often the case that such dependencies can be factorized in a non-trivial way, and distinct variables interact only ‘locally’. This important structural property plays a crucial role. It is described here in a graphical language — the one of factor graphs. Ensembles of probability distributions naturally map to ensemble of random graphs, or hypergraphs. Several basic properties of these ensembles are discussed, from the appearance of a giant component to the motifs appearing in their local structure. The graph description is a necessary background for the understanding of message passing algorithms.

Keywords:   factor graph, random graph, random hypergraph, giant component, motif

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