Most email cliques vanish within a month: temporal graph networks only match last month's value, and a survival probability does the real work

Forecasting group tension in an email network first requires knowing whether the group still exists next month; in this data most cliques disappear within one month, leaving the target undefined for most rows. The earlier clique-conflict scores were computed on a single static graph, with no cross-month tracking and no handling of targets lost when groups dissolve. Of 689 retained cliques, 278 (40.3%) have a one-to-one successor at Jaccard threshold 0.5 and 411 (59.7%) do not; scoring dissolved cliques as zero rewards models that predict small values, while scoring only survivors uses information known after the forecast.

Carrying the current tension forward is the forecast hardest to beat on this data. Neural models with a residual output start at persistence and only have to learn a correction, yet after training they stay near persistence rather than passing it. Over 24 rolling origins and 237 surviving cliques, persistence has MSE 11.56; the residual MLP ratio is 0.96, residual GCN and SAGE 1.00, GCN+GRU 1.02, none significant after Holm adjustment; the plain GCN is 1.15, GBDT 1.12 and GBDT with neighbour aggregates 1.17.

What lowers deployable forecast error is the survival probability, not a more elaborate tension model. Under the deployable protocol persistence alone is not a fair reference because it assigns tension to groups about to disappear, so the comparison baseline becomes persistence times the training base survival rate. Over 614 cliques, persistence times the base rate has MSE 19.42 and persistence times the hazard-model survival probability 16.20 (ratio 0.83, interval [0.76, 0.94]); the gain comes from the dissolved part falling from 10.8 to 5.8 while the survivor part rises only from 8.6 to 10.4.

How groups are defined contributes a substantial share of the apparent turnover, and more than half of retained cliques are exactly one email's recipient list. Across five definitions, including cliques not contained in one email, repeated-pair cliques, clique percolation and Louvain communities, survival stays between 30.5% and 43.8%, and none lifts it above one half. In 55.3% of retained cliques the member set coincides with the Enron participant list of a single email in that window; raising the Jaccard threshold from 0.3 to 0.7 drops survival from 56% to 22%, while the K′ cap and window length move it by only a few points.

The conclusions rest on the Enron simplicial email data: 148 employee IDs, 10,883 emails and 44 thirty-day snapshots, of which 39 transitions carry targets, evaluated over 24 rolling origins. The setting is a single company, a single one-month horizon, and clique tension plus person-level risk ranking; the source proposes tracking hyperedges directly and testing whether the results carry over on a second dataset with department labels such as email-Eu-core.

The source describes a small dataset: 39 usable months and 689 cliques, with early origins trained on a few dozen survivors, so models with more parameters are at a disadvantage at this scale and a larger network might give a different answer. With the normalized target the neural models are mostly worse and only a two-parameter linear model beats persistence, and those differences do not survive Holm adjustment; in the deployable setting the hazard-weighted interval excludes 1 but the Holm-adjusted Diebold–Mariano p-value is 0.54. Whether ICCS and SRI actually measure silos remains unverified, and SRI correlates with clique membership count at Spearman 0.82.