Soft configuration model

Part of a series on
Network science
Theory
Graph Complex network Contagion Small-world Scale-free Community structure Percolation Evolution Controllability Graph drawing Social capital Link analysis Optimization Reciprocity Closure Homophily Transitivity Preferential attachment Balance theory Network effect Social influence
Network types
Informational (computing) Telecommunication Transport Social Scientific collaboration Biological Artificial neural Interdependent Semantic Spatial Dependency Flow on-Chip
Graphs
Features Clique Component Cut Cycle Data structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random Weighted
Metrics Algorithms
Centrality Degree Motif Clustering Degree distribution Assortativity Distance Modularity Efficiency
Models
Topology Random graph Erdős–Rényi Barabási–Albert Bianconi–Barabási Fitness model Watts–Strogatz Exponential random (ERGM) Random geometric (RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft configuration LFR Benchmark Dynamics Boolean network agent based Epidemic/SIR
Lists Categories
Topics Software Network scientists Category:Network theory Category:Graph theory
v t e

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 ${\displaystyle n}$ 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.