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Wednesday, 4 November 2026: 1 new paper, 1 cross-list and 4 replacements in Social and Information Networks (cs.SI), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
Exponential-family random graph models ERGMs provide a parametric interpretable framework for modeling real graphs including the Web and social networks Fitted ERGMs may suffer from degeneracy matching observed graph statistics in expectation does not guarantee that the observed graph and similar ones are highly probable under the fitted distribution We introduce Band-Concentrated ERGMs BaCon a framework that avoids degeneracy by imposing a probabilistic constraint requiring at least $1-\delta$ of the distribution probability mass to lie on the set of graphs with statistics within an $\varepsilon$-tolerance band around the observed statistics BaCons maximumentropy distribution still belongs to the exponential family while including a factor checking for inclusion in the tolerance band We derive the exact Metropolis-Hastings acceptance rule for this target and use a practical stochastic approximation procedure with a smoothed band membership during fitting Experiments on social networks across increasingly challenging model specifications show that BaCon substantially increases the probability mass assigned to graphs whose statistics are close to the observed ones while remaining estimable for specifications where standard ERGM estimation fails These results demonstrate that probability mass constraints are a principled way to mitigate degeneracy while retaining the benefits of exponential-family graph models
Predicting social network churn before it becomes visible in aggregate metrics remains an open challenge, particularly in enterprise settings where heterogeneous usage patterns, sparse data, and deployment constraints preclude standard supervised approaches. We formalize this problem as finite-step engagement projection over contributor-role Markov chains, with a stationary-distribution interpretation for ergodic chains in the long-run limit. For each engagement feature type within a network (e.g., Q&A, communities, articles, etc.), users are classified monthly into four behavioral states and a transition matrix is estimated from six months of history. Six-step propagation yields a label-free projection of the contributor mix; for ergodic chains, the Perron-Frobenius theorem establishes convergence under repeated propagation. Comparing projected future engagement to current engagement produces the Health Ratio, a single score requiring no trained model, no labels, and no infrastructure beyond SQL. Validated across seven rolling prediction windows on 11,500+ tenant-level networks, the Health Ratio achieves mean AUC 0.917 with a 156 times churn-rate gradient across risk tiers, outperforming all single-signal baselines and the growth-adjusted variant previously deployed in production. An ablation study shows that six-step propagation achieves similar churn discrimination to the eigenvector-based score. Deployed on Microsoft Engage since October 2025, the framework powers customer health monitoring and has enabled proactive intervention on at-risk networks before decline becomes visible in traditional metrics.