The paper reviews several Complex Network Theory (CNT) based methodologies to model and analyze interconnected networks. To address the deficiencies reported in past studies, an advanced model of coupled Electric Power System (EPS) and Information and Communication Technology (ICT) is developed. The new model is designed as a three-dimensional graph with edges and nodes, and it highlights the interaction and interdependency of both EPS and ICT. The criticality of each component within the interconnected system is investigated by analyzing the efficiency-weighted node degree of each node symbolizing the components. The model has been tested on an ICT supported 14-Bus distribution network under three different loading conditions. Results show that the coupled infrastructure complies with the typical characteristics of scale-free network . It is also shown the ICT system, although smaller in scale, contains more critical hubs than the power distribution network. The results of the proposed approach can be used as a reference to analyze the criticality in other coupled infrastructure by incorporating the internal characteristics of coupled systems.