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{{for|use in ecology|Theoretical ecology}}
In mathematics, for example in the study of statistical properties of [[Graph (discrete mathematics)|graphs]], a '''null model''' is type of random object that matches one specific object in some of its features, or more generally satisfies a collection of constraints, but which is otherwise taken to be an unbiasedly random structure. The null model is used as a term of comparison, to verify whether the object in question displays some non-trivial features (properties that wouldn't be expected on the basis of chance alone or as a consequence of the constraints), such as [[community structure]] in graphs. An appropriate null model behaves in accordance with a reasonable [[null hypothesis]] for the behavior of the system under investigation.
One null model of utility in the study of [[complex networks]] is that proposed by Newman and [[Michelle Girvan|Girvan]], consisting of a randomized version of an original graph <math>G</math>, produced through edges being 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|author2=M.Girvan |author2-link= Michelle Girvan |title=Finding and evaluating community structure in networks|journal=Phys. Rev. E|year=2004|volume=69|issue=2|doi=10.1103/physreve.69.026113 |arxiv=cond-mat/0308217|bibcode=2004PhRvE..69b6113N|pmid=14995526|page=026113}}</ref>
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