The electrostatic discharge (ESD) problem has become a challenging reliability issue in nanometer circuit design. High voltages resulted from ESD might cause high current densities in a small device and burn it out, so on-chip protection circuits for IC pads are required. To reduce the design cost, the protection circuit should be added only for the IC pads with an ESD current path, which arises the ESD current path analysis problem. In this paper, we first introduce the analysis problem for ESD protection in circuit design. We then model the circuit as a constrained graph, decompose ESD connected components linked with the pads, and apply the breadth-first search (BFS) to identify the ESD connected components in each constrained graph and thus the current paths. Experimental results show that our algorithm can detect all ESD paths very efficiently and economically. To our best knowledge, our algorithm is the first point tool available to the public for the ESD analysis.