Soft configuration model

In applied mathematics, the soft configuration model (SCM) is a random graph model subject to the principle of maximum entropy under constraints on the expectation of the degree sequence of sampled graphs. Whereas the configuration model (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 ${\displaystyle n}$ has a nonzero probability of sampling any graph of size ${\displaystyle n}$, whereas the CM is restricted to only graphs having precisely the prescribed connectivity structure.