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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.[1] 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[2]). The SCM for graphs of size has a nonzero probability of sampling any graph of size , whereas the CM is restricted to only graphs having precisely the prescribed connectivity structure.

  1. ^ van der Hoorn, Pim; Gabor Lippner; Dmitri Krioukov (2017-10-10). "Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution". arXiv:1705.10261.
  2. ^ Garlaschelli, Diego; Frank den Hollander; Andrea Roccaverde (January 30, 2018). "Coviariance structure behind breaking of ensemble equivalence in random graphs" (PDF). Archived (PDF) from the original on February 4, 2023. Retrieved September 14, 2018.