Table reasoning, a task to answer questions by reasoning over data presented in tables, is an important topic due to the prevalence of knowledge stored in tabular formats. Recent solutions use Large Language Models (LLMs), exploiting the semantic understanding and reasoning capabilities of LLMs. A common paradigm of such solutions linearizes tables to form plain texts that are served as input to LLMs. This paradigm has critical issues. It loses table structures, lacks explicit reasoning paths for result explainability, and is subject to the "lost-in-the-middle" issue. To address these issues, we propose Table Graph Reasoner (TABGR), a training-free model that represents tables as an Attributed Table Graph (ATG). The ATG explicitly preserves row-column-cell structures while enabling graph-based reasoning for explainability. We further propose a Question-Guided Personalized PageRank (QG-PPR) mechanism to rerank tabular data and mitigate the lost-in-the-middle issue. Extensive experiments on two commonly used benchmarks show that TABGR consistently outperforms state-of-the-art models by up to 9.7% in accuracy. Our code will be made publicly available upon publication.