Large language model (LLM)-based agents increasingly connect model-generated decisions to security-sensitive software capabilities such as command execution, filesystem access, network communication, browser control, and external tools. Existing analyses often use predefined sensitive operations as anchors, but operation identity alone is insufficient to determine security implications. We present AgentSecGraph, a security-aware static analysis framework that constructs a candidate-centered Security-Aware Agent Dependency Graph (Security-ADG) for each security-sensitive operation. It augments operation identity with agent relevance, source and dependency evidence, trust-boundary context, guard evidence, and external-effect semantics. We further introduce AgentSecBench, a corpus of 67 real-world LLM-agent repositories spanning 11 ecosystems and 37,542 source files. The current analyzer identifies 23,866 static security-sensitive operation candidates across 65 repositories and emits one Security-ADG artifact per candidate. Corpus-wide analysis recovers source-to-operation dependency evidence for 9,821 candidates (41.15%) and potential guard evidence for 3,075 (12.88%), completing in 50.8 minutes. Using a separate reproduction-backed evaluation layer, we establish 22 security-sensitive behaviors across 13 repositories: one confirmed vulnerability, one pending disclosure candidate, and 20 guarded behaviors. In nine held-out cases, Security-ADG preserves 91.1% of the reference context and all five observed guards, compared with 20.0% for a sink-only view and 40.0% for a simplified ADG. These results show that security-aware dependency and contextual evidence enable distinctions that cannot be recovered from sensitive-operation identity alone.

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