Zero-shot reasoning on text-rich networks (TRNs) remains a challenging frontier, as models must integrate textual semantics with relational structure without task-specific supervision. While graph neural networks rely on fixed label spaces and supervised objectives, recent large language model (LLM)-based approaches often overlook graph context or depend on distillation from larger models, limiting generalisation. We propose TRN-R1-Zero, a post-training framework for TRN reasoning trained solely via reinforcement learning. TRN-R1-Zero directly optimises base LLMs using a Neighbour-aware Group Relative Policy Optimisation objective that dynamically adjusts rewards based on a novel margin gain metric for the informativeness of neighbouring signals, effectively guiding the model toward relational reasoning. Unlike prior methods, TRN-R1-Zero requires no supervised fine-tuning or chain-of-thought data generated from large reasoning models. Extensive experiments across citation, hyperlink, social and co-purchase TRN benchmarks demonstrate the superiority and robustness of TRN-R1-Zero. Beyond cross-domain transfer, TRN-R1-Zero, trained solely on node-level tasks, further generalises to edge- and graph-level tasks in a zero-shot manner. The codebase is open-source at [https://github.com/superallen13/TRN-R1-Zero](https://github.com/superallen13/TRN-R1-Zero).

Out-of-distribution (OOD) detection remains challenging in text-rich networks, where textual features intertwine with topological structures. Existing methods primarily address label shifts or rudimentary domain-based splits, overlooking the intricate textual-structural diversity. For example, in social networks, where users represent nodes with textual features (name, bio) while edges indicate friendship status, OOD may stem from the distinct language patterns between bot and normal users. To address this gap, we introduce the TextTopoOOD framework for evaluating detection across diverse OOD scenarios: (1) attribute-level shifts via text augmentations and embedding perturbations; (2) structural shifts through edge rewiring and semantic connections; (3) thematically-guided label shifts; and (4) domain-based divisions. Furthermore, we propose TNT-OOD to model the complex interplay between Text aNd Topology using: 1) a novel cross-attention module to fuse local structure into node-level text representations, and 2) a HyperNetwork to generate node-specific transformation parameters. This aligns topological and semantic features of ID nodes, enhancing ID/OOD distinction across structural and textual shifts. Experiments on 11 datasets across four OOD scenarios demonstrate the nuanced challenge of TextTopoOOD for evaluating OOD detection in text-rich networks.