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Networks may need to be interconnected for various reasons such as inter-organizational communication, redundant connectivity, increasing data-rate and minimizing delay or packet-loss, etc. However, the trustworthiness of an added interconnection link cannot be taken for granted due to the presence of attackers who may compromise the security of an interconnected network by intercepting the interconnections. Namely, an intercepted interconnection link may not be secured due to the data manipulations by attackers. In the first part of this dissertation, the number of interconnections between the two networks is optimized for maximizing the data-rate and minimizing the packet-loss under the threat of security attacks. The optimization of the interconnectivity considering the security attack is formulated using a rate-distortion optimization setting, as originally introduced by Claude E. Shannon in the information theory. In particular, each intercepted interconnection is modeled as a noisy communication channel where the attackers may manipulate the data by flipping and erasing of data bits, and then the total capacity for any given number of interconnections is calculated. By exploiting such formulation, the optimal number of interconnections between two networks is found under network administrators data-rate and packet-loss requirement, and most importantly, without compromising the data security. It is concluded analytically and verified by simulations under certain conditions, increasing interconnections beyond an optimal number would not be beneficial concerning the data-rates and packet-loss. In the second part of this dissertation, the vulnerability of the interconnected network is analyzed by a probabilistic model that maps the intensity of physical attacks to network component failure distributions. Also, assuming the network is susceptible to the attack propagation, the resiliency of the network is modeled by the influence model and epidemic model. Finally, a stochastic model is proposed to track the node failure dynamics in a network considering dependency with power failures. Besides, the cascading failure in the power grid is analyzed with a data-driven model that reproduces the evolution of power-transmission line failure in power grids. To summarize, the optimal interconnectivity among networks is analyzed under security attacks, and the dynamic interactions in an interconnected network are investigated under various physical and logical attacks. The proper application of this work would add the minimum number of inter-network connections between two networks without compromising the data security. The optimal number interconnections would meet network administrator’s requirement and minimize cost (both security and monetary) associated with unnecessary connections. This work can also be used to estimate the reliability of a communication network under different types of physical attacks independently and also by incorporating the dynamics of power failures.