GECKO: A Diagnostic Benchmark for Federated Continual Learning on a Shared Graph

Federated continual graph learning (FCGL) studies how distributed clients learn a sequence of graph prediction tasks without forgetting earlier knowledge. Evaluating FCGL is challenging because the way graph data are assigned to clients can change both the prediction examples and the graph context available locally, while task order introduces a separate source of variation over time. We introduce GECKO (Graph Evaluation of Client-Knowledge and Order Sequences), a diagnostic benchmark for FCGL on a fixed graph distributed across clients. GECKO defines matched evaluation settings across node classification, link classification, and link prediction under Task-, Class-, and Domain-Incremental Learning. It varies client allocation and task order under explicit comparison rules, combining construction checks with diagnostics of task acquisition, forgetting, and cross-client support. Across the evaluated settings, both factors substantially affect final performance and forgetting, and their effects differ across methods and prediction problems. These results show that FCGL methods should be assessed across multiple allocation and task-order conditions rather than a single partition and sequence. GECKO provides reusable protocols and diagnostics for interpreting these comparisons.