Soft configuration model

<p>In applied mathematics, the soft configuration model (SCM) is a <a href="/facts/Random_graph/gfQhq1Sz">random graph</a> model subject to the <a href="/facts/Principle_of_maximum_entropy/T0gybmPF">principle of maximum entropy</a> under constraints on the <a href="/facts/Expectation_value/1XV0JKL8">expectation</a> of the <a href="/facts/Degree_sequence/LnFFpI8v">degree sequence</a> of sampled <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graphs</a>. Whereas the <a href="/facts/Configuration_model/9MolJJeV">configuration model</a> (CM) uniformly samples random graphs of a specific degree sequence, the SCM only retains the specified degree sequence on average over all network realizations; in this sense the SCM has very relaxed constraints relative to those of the CM ("soft" rather than "sharp" constraints). The SCM for graphs of size 
  
    
      
        n
      
    
    {\displaystyle n}
  
 has a nonzero probability of sampling any graph of size 
  
    
      
        n
      
    
    {\displaystyle n}
  
, whereas the CM is restricted to only graphs having precisely the prescribed connectivity structure.
</p>

Soft configuration model open-in-new

Soft configuration model