This paper provides a review of the research conducted on complex network analysis (CNA) in electric power systems. Moreover, a new approach is presented to find optimal locations for microgrids (MGs) in electric distribution systems (EDS) utilizing complex network analysis. The optimal placement in this paper points to the location that will result in enhanced grid resilience, reduced power losses and line loading, better voltage stability, and a supply to critical loads during a blackout. The criteria used to point out the optimal placement of the MGs were predicated on the centrality analysis selected from the complex network theory, the center of mass (COM) concept from physics, and the recently developed controlled delivery grid (CDG) model. An IEEE 30 bus network was utilized as a case study. Results using MATLAB (MathWorks, Inc., Nattick, MA, USA) and PowerWorld (PowerWorld Corporation, Champaign, IL, USA) demonstrate the usefulness of the proposed approach for MGs placement.