Chain-of-thought (CoT) prompting has achieved remarkable success in natural language processing (NLP). However, its vast potential remains largely unexplored for graphs. This raises an interesting question: How can we design CoT prompting for graphs to guide graph models to learn step by step? On one hand, unlike natural languages, graphs are non-linear and characterized by complex topological structures. On the other hand, many graphs lack textual data, making it difficult to formulate language-based CoT prompting. %Therefore we cannot directly adopt the CoT prompting methods used in the language domain. In this work, we propose the first CoT prompt learning framework for text-free graphs, GCoT. Specifically, we decompose the adaptation process for each downstream task into a series of inference steps, with each step consisting of prompt-based inference, ''thought'' generation, and thought-conditioned prompt learning. While the steps mimic CoT prompting in NLP, the exact mechanism differs significantly. Specifically, at each step, an input graph, along with a prompt, is first fed into a pre-trained graph encoder for prompt-based inference. We then aggregate the hidden layers of the encoder to construct a ''thought'', which captures the working state of each node in the current step. Conditioned on this thought, we learn a prompt specific to each node based on the current state. These prompts are fed into the next inference step, repeating the cycle. To evaluate and analyze the effectiveness of GCoT, we conduct comprehensive experiments on eight public datasets, which demonstrate the advantage of our approach.

Graphs are able to model interconnected entities in many online services, supporting a wide range of applications on the Web. This raises an important question: How can we train a graph foundational model on multiple source domains and adapt to an unseen target domain? A major obstacle is that graphs from different domains often exhibit divergent characteristics. Some studies leverage large language models to align multiple domains based on textual descriptions associated with the graphs, limiting their applicability to text-attributed graphs. For text-free graphs, a few recent works attempt to align different feature distributions across domains, while generally neglecting structural differences. In this work, we propose a novel Structure Alignment framework for text-free Multi-domain Graph Pre-Training and cross-domain adaptation (SAMGPT). It is designed to learn multi-domain knowledge from graphs originating in multiple source domains, which can then be adapted to address applications in an unseen target domain. Specifically, we introduce a set of structure tokens to harmonize structure-based aggregation across source domains during the pre-training phase. Next, for cross-domain adaptation, we design dual prompts, namely, holistic prompts and specific prompts, which adapt unified multi-domain structural knowledge and fine-grained, domain-specific information, respectively, to a target domain. Finally, we conduct comprehensive experiments on seven public datasets to evaluate and analyze the effectiveness of SAMGPT.

Graph Neural Networks (GNNs) have emerged as a mainstream technique for graph representation learning. However, their efficacy within an end-to-end supervised framework is significantly tied to the availability of task-specific labels. To mitigate labeling costs and enhance robustness in few-shot settings, pre-training on self-supervised tasks has emerged as a promising method, while prompting has been proposed to further narrow the objective gap between pretext and downstream tasks. Although there has been some initial exploration of prompt-based learning on graphs, they primarily leverage a single pretext task, resulting in a limited subset of general knowledge that could be learned from the pre-training data. Hence, in this paper, we propose MultiGPrompt, a novel multi-task pre-training and prompting framework to exploit multiple pretext tasks for more comprehensive pre-trained knowledge. First, in pre-training, we design a set of pretext tokens to synergize multiple pretext tasks. Second, we propose a dual-prompt mechanism consisting of composed and open prompts to leverage task-specific and global pre-training knowledge, to guide downstream tasks in few-shot settings. Finally, we conduct extensive experiments on six public datasets to evaluate and analyze MultiGPrompt.