This paper proposes a graph-based retrieval technique on a weighted co-citation network, which allows users to find more relevant documents easily from the co-citation network. More specifically, the random walk with restart technique is applied to a weighted graph of documents, in which the degree of each edge weight is measured by the number of co-citation documents and the strength of the cocitation context; both obtained by parsing the full text of the citing documents. To evaluate its effectiveness empirically, a special test collection was created from the Open Access Subset of PubMed Central, and the search performance of the proposed method was compared with traditional cocitation searching by "precision at k." The experimental results indicate that the proposed method tends to retrieve much more relevant documents without reducing precision.