This paper introduces an analytical method, based on the Complex Network Theory (CNT), to assess the risk of the Smart Grid failure due to communication network malfunction, associated with latency and ICT network reliability. Firstly, the communication architecture is modelled using a two-step CNT frameworkan Operation Graph (OG) in step one and a Reliability Graph (RG) in step two. Secondly, the latency of data packets and the reliability of each communication device are incorporated into the model to identify the reliability of all operational communication paths for successful power system control purposes. Then, the risk of Smart Grid failure due to the communication network malfunction is quantified using a System Reliability Index (SRI). Next, sensitivity analysis is performed to assess the importance of each communication network component using two innovative Importance Measures (IM), namely System Reliability Advancement Worth (SRAW) and System Reliability Deterioration Worth (SRDW). Finally, the proposed approach is demonstrated on a laboratory-scale communication network.