Feeder routing and reliability assessment are essential for effective distribution network planning. However, excessively long feeders can lead to increased costs and decreased reliability. To enhance economic and reliability performance, this paper proposes a reliability-centered planning method for feeder routing and conductor sizing. Specifically, a graph-based fictitious power flow model is constructed within the geographic graph. Overlapping feeder routes powered by fictitious power flows from multiple sources are designated as line connection. These feeder routes, constrained by the geographic graph, are interconnected via line connection to form a mesh network structure. To meet the requirements of reliability-centered optimization, the affiliation variables are introduced. Based on the affiliation variables, the algebraic formula is embedded into the fictitious power flow model to enable the calculation of reliability during the optimization process. By incorporating customized reliability-related constraints in the model, the specific reliability objectives can be achieved. In addition, the non-convex terms in the fictitious power flow model are relaxed into convex forms, and certain variable products are replaced with auxiliary variables, allowing the problem to be solved by an off-the-shelf solver. Finally, the proposed method is tested on two case studies, demonstrating its effectiveness.