Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains. Unlike traditional Graph Neural Networks (GNNs), which are typically trained from scratch for specific tasks on particular datasets, GFMs face the challenge of effectively leveraging vast and diverse graph data to achieve positive transfer. Inspired by foundation models in computer vision (CV) and natural language processing (NLP), the paper proposes a "graph vocabulary" perspective, where basic transferable units underlying graphs encode invariance on graphs. The graph vocabulary is constructed based on network analysis, expressiveness, and stability, potentially advancing future GFM design in line with neural scaling laws. Existing GFMs, such as ULTRA and OFA, have achieved initial success, including zero-shot generalization to unseen graphs. These models are categorized into task-specific, domain-specific, and primitive GFMs. ULTRA, a task-specific GFM for knowledge graph completion, utilizes the NBFNet backbone model, which enables inductive generalization through an expressive relational vocabulary. The graph of relations, theoretically grounded, helps connect new unseen relationship types to existing ones, enabling positive transfer. The key to successful GFM design lies in finding invariance across diverse graph data into the same representation space. The paper discusses transferability principles in node classification, link prediction, and graph classification, emphasizing the importance of network analysis, expressiveness, and stability. It also explores the feasibility of GFMs following neural scaling laws, highlighting the need for data scaling, model scaling, and leveraging large-scale language models (LLMs) for graph tasks. The paper concludes that GFMs have the potential to reduce resource consumption and manual annotation in various domains, offering a versatile and fair approach to graph-based applications. The research highlights the importance of a universal graph vocabulary and the challenges in developing GFMs that can effectively cater to a broad spectrum of graph-based applications. The paper also emphasizes the need for further research in this evolving field, including the broader usage of GFMs in other domains and the feasibility of GFMs in different scenarios.Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains. Unlike traditional Graph Neural Networks (GNNs), which are typically trained from scratch for specific tasks on particular datasets, GFMs face the challenge of effectively leveraging vast and diverse graph data to achieve positive transfer. Inspired by foundation models in computer vision (CV) and natural language processing (NLP), the paper proposes a "graph vocabulary" perspective, where basic transferable units underlying graphs encode invariance on graphs. The graph vocabulary is constructed based on network analysis, expressiveness, and stability, potentially advancing future GFM design in line with neural scaling laws. Existing GFMs, such as ULTRA and OFA, have achieved initial success, including zero-shot generalization to unseen graphs. These models are categorized into task-specific, domain-specific, and primitive GFMs. ULTRA, a task-specific GFM for knowledge graph completion, utilizes the NBFNet backbone model, which enables inductive generalization through an expressive relational vocabulary. The graph of relations, theoretically grounded, helps connect new unseen relationship types to existing ones, enabling positive transfer. The key to successful GFM design lies in finding invariance across diverse graph data into the same representation space. The paper discusses transferability principles in node classification, link prediction, and graph classification, emphasizing the importance of network analysis, expressiveness, and stability. It also explores the feasibility of GFMs following neural scaling laws, highlighting the need for data scaling, model scaling, and leveraging large-scale language models (LLMs) for graph tasks. The paper concludes that GFMs have the potential to reduce resource consumption and manual annotation in various domains, offering a versatile and fair approach to graph-based applications. The research highlights the importance of a universal graph vocabulary and the challenges in developing GFMs that can effectively cater to a broad spectrum of graph-based applications. The paper also emphasizes the need for further research in this evolving field, including the broader usage of GFMs in other domains and the feasibility of GFMs in different scenarios.