Retrieval Augmented Generation (RAG) is an essential agent for Large Language Model (LLM) aided Description Language (HDL) tasks, addressing the challenges of limited training data and prohibitively long prompts. However, its performance in handling ambiguous queries and real-world, repository-level HDL projects containing thousands or even tens of thousands of code lines remains limited. Our analysis demonstrates two fundamental mismatches, structural and vocabulary, between conventional semantic similarity-based RAGs and HDL codes. To this end, we propose HDLxGraph, the first framework that integrates the inherent graph characteristics of HDLs with RAGs for LLM-assisted tasks. Specifically, HDLxGraph incorporates Abstract Syntax Trees (ASTs) to capture HDLs' hierarchical structures and Data Flow Graphs (DFGs) to address the vocabulary mismatch. In addition, to overcome the lack of comprehensive HDL search benchmarks, we introduce HDLSearch, an LLM generated dataset derived from real-world, repository-level HDL projects. Evaluations show that HDLxGraph improves search, debugging, and completion accuracy by 12.04%/12.22%/5.04% and by 11.59%/8.18%/4.07% over state-of-the-art similarity-based RAG and software-code Graph RAG baselines, respectively. The code of HDLxGraph and HDLSearch benchmark are available at https://github.com/UMN-ZhaoLab/HDLxGraph.