Efficacy of Geoenergy storage is contingent upon the presence of well-developed natural fractures (NF) within the reservoir, which is the medium of energy storage and the channel of migration. Electrical imaging logging (EIL) and advancing Artificial intelligence (AI) technologies offer dependable NF detection methodologies, while several limitations persist: 1) Incomplete onsite data inhibit the performance of above methods, that is, the lacking of prior knowledge makes it difficult to remove the noise generated from pores-vugs-muds attached to fractures. 2) NFs within images are represented by normal pixels, neglecting hidden spatial features and correlations between adjacent fractures, which results in partial identification of discontinuous NFs containing multiple missing elements. Consequently, an incomplete natural fracture detection method via prior-knowledge graph from electric imaging logging is proposed. Firstly, through pixel-node transformation, path-graphs constructed from connections between nodes and their neighbors in morphological path can effectively capture spatial-geological features of NFs. Secondly, based on distinct geological characteristics of NFs and corresponding background noises, multiple thresholds are established to evaluate each node within the path-graph while removing extraneous nodes related to pores, vugs, and muds. Subsequently, a graph contrastive learning (GCL) model is adopted to extract information across different path-graphs based on spatial-geological features and assign varying matching labels to nodes accordingly. Finally, integrated graphs are constructed by splicing path-graphs through recombination of nodes sharing identical labels that correspond to continuous NFs. The efficacy of the proposed method is validated through comprehensive comparative tests using onsite EIL data.