The aftermath of including new technologies in a modern electric system in conjunction with the incessant rise in power demand could pose a risk to the optimal operation of the system. Therefore, it becomes imperative to identify the most influential and critical nodes of such a system to avert future problems in network operation. In this paper, to identify most significant nodes of the system, the authors propose two measures of centrality in accordance with the network structural properties of a power system, namely, degree centrality (DC) and eigenvector centrality (EC). These are expressed considering the admittance matrix that exists among the interconnection of load to load nodes in an electrical power network. A critical node closeness centrality (CNCC) method is also proposed to identify critical nodes of the system. This is done by modifying the conventional closeness centrality (CC) to include the influence of interconnection that exists between network load to load nodes as captured by the admittance matrix between them. A comparative analysis of the proposed techniques with other conventional methods is also carried out. The result of the simulation shows that the proposed methods could serve as alternative tools in the identification of influential and weak nodes in a power system.