A configuration of the triple $(\mathcal{P}, \mathcal{L}, \mathcal{I})$ on the incidence relation which holds the properties of "Any two points are incident with at most one line" and "Any two lines are incident with at most one point". In projective geometry, bipartite graphs can be used as an incidence model between the points and the lines of a configuration. The graphs associated with a space are a good tool for understanding the topological and geometric properties of the space. in abstract systems. In this paper, we define a novel graph associated with circular space and obtain its properties in terms of some pure-graph invariants. Also, we characterize it regarding the graph associated with other spaces in the literature.