Graph databases are often used to manage relationship-rich data, whose graph structure and attributes may be sensitive. In many applications, a database owner or a service provider evaluates queries over a private graph for a client. Because the graph cannot be fully disclosed and independently re-executing the query may be impractical, the client cannot directly verify the returned result. This creates a need for verifiable graph query evaluation that preserves data confidentiality. We present VerfGraph, a zero-knowledge system for verifiable graph query evaluation, which enables a client to verify that the query result was correctly computed over a committed graph data, without revealing private graph records or intermediate query values beyond the public inputs and what is implied by the query result. Building on the expansion-centric model introduced by the state-of-the-art zero-knowledge verifiable graph query evaluation system ZKGraph (ICDE'26), VerfGraph achieves more efficient and expressive zero-knowledge verifiable graph query evaluation by advancing design in two key ways. First, we propose novel operator-proof methods for core expansion and shortest-path operations that reduce costly sorting and comparison checks and eliminate edge canonicalization for bidirectional expansion. Furthermore, we introduce correctness proofs for count and weighted shortest-path operators, broadening the class of graph queries that can be verified. We evaluate VerfGraph using the LDBC Social Network Benchmark. Compared with ZKGraph on complex IC queries, VerfGraph achieves $33.9\times$-$59.7\times$ speedups in proof generation and reduces peak prover memory by factors of $4.5\times$-$6.6\times$, while maintaining millisecond-level verification and producing sub-MB proofs.

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