Null model: Difference between revisions

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In mathematics, in the study of statistical properties of [[Graph (mathematics)|graphs]], the '''null model''' is a graph which matches one specific graph in some of its structural features, but which is otherwise taken to be an instance of a [[random graph]]. The null model is used as a term of comparison, to verify whether the graph in question displays some feature, such as community structure, or not.

One null model is that proposed by Newman and Girvan and consists of a randomized version of the original graph, where edges are rewired at random, under the constraint that the expected degree of each vertex matches the degree of the vertex in the original graph.<ref>{{cite journal|last=M.E.J|first=Newman|coauthorsauthor2=M.Girvan |title=Finding and evaluating community structure in networks|journal=Phys. Rev. E|year=2004|volume=69|issue=2}}</ref>

The null model is the basic concept behind the definition of [[Modularity (networks)|modularity]], a function which evaluates the goodness of partitions of a graph into clusters.