Introducing the KERGM: an ERG model immune to degeneracy

Bart Blackburn


At the forefront of network modeling is the Exponential Random Graph Model (ERGM), broadly appealing due to its tractability, interpretability, and flexibility in incorporating almost any network characteristics. However, ERGMs are known to suffer from degeneracy, in which case they may give disproportionate mass to extremal configurations and exhibit a severe lack of fit to the observed network data. This talk introduces the kurtosis-constrained exponential random graph model (KERGM), a new model class which can be viewed as an extension of the standard ERGM but which is not susceptible to degeneracy. We motivate the KERGM from a maximum entropy framework as well as from an understanding of the kurtosis in this setting. We prove that the KERGM is non-degenerate and show that it still retains all of the desirable qualities of the ERGM mentioned above. We then demonstrate the effectiveness of KERGMs on several real-world networks which otherwise defy modeling using standard ERGMs. With excellent results and strong theoretical justification, we make the case for the KERGM to supplant the ERGM entirely.

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