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Existing solutions rely on training external graph-based adapters or fine-tuning, which incur high costs and lost generalizability. In this work, we investigate the internal mechanisms of LLMs and present a critical finding: LLMs spontaneously reconstruct the graph's topology internally, evidenced by a distinct \"sawtooth\" pattern in their attention maps that structurally aligns with the \"token-level adjacency matrix\". However, this intrinsic structural understanding is diluted by the attention sink. We theoretically formalize this dilution as a representation bottleneck, stemming from a fundamental conflict: the model's anisotropic bias, essential for language tasks, suppresses the topology-aware local aggregation required for graph reasoning. 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