Core Concepts
The authors propose an extension to the existing Stochastic Degree Sequence Model (SDSM) that allows the null model to include edge constraints (EC) such as prohibited edges, enabling more accurate backbone extraction from bipartite network projections.
Abstract
The authors introduce the Stochastic Degree Sequence Model with Edge Constraints (SDSM-EC), an extension of the existing SDSM that can accommodate edge constraints in the form of prohibited edges. Prohibited edges arise in bipartite networks when a given agent cannot be connected to a given artifact, for example, due to the agent's absence or legal restrictions.
The authors first demonstrate the SDSM-EC in a toy example, showing how it correctly omits noisy edges from the backbone compared to the conventional SDSM, which assumes no edge constraints. They then illustrate the practical application of SDSM-EC using empirical data on young children's play interactions, where two types of prohibited edges exist due to the school's organization into age-based classrooms and attendance schedules.
The results show that the SDSM-EC backbone contains fewer edges than the SDSM backbone, as it correctly omits edges that appear significant under the SDSM's broader null model but are not significant when the proper edge constraints are considered. The authors recommend using SDSM-EC to extract backbones of bipartite projections when the bipartite network contains prohibited edges.
The authors also discuss the potential to extend the SDSM-EC to accommodate another type of edge constraint, required edges, where a given agent must always be connected to a given artifact. They identify areas for future research, including improving the estimation of the probability matrix Q under SDSM-EC and investigating the feasibility of incorporating other types of constraints in bipartite null models.
Stats
The cardinality of the space of matrices with row sums {1,1,2,2} and column sums {1,1,2,2} and one or two cells constrained to zero is much smaller than the cardinality of the space without constrained cells.
The deviation between the true and estimated Qik for all such constrained spaces tends to be small.