Critical infrastructure systems are essential for the continuous functionality of modern global societies. Some examples of these systems include electric energy, potable water, oil and gas, telecommunications, and the internet. Different topologies underline the structure of these networked systems. Each topology (i.e., physical layout) conditions the way in which networks transmit and distribute their flow. Also, their ability to absorb unforeseen natural or intentional disruptions depends on complex relations between network topology and optimal flow patterns. Most of the current research on large networks is focused on understanding their properties using statistical physics, or on developing advanced models to capture network dynamics. Despite these important research efforts, almost all studies concentrate on specific networks. This network-specific approach rules out a fundamental phenomenon that may jeopardize the performance predictions of current sophisticated models: network response is in general interdependent, and its performance is conditioned on the performance of additional interacting networks. Although there are recent conceptual advances in network interdependencies, current studies address the problem from a high-level point of view. For instance, they discuss the problem at the macro-level of interacting industries, or utilize economic input-output models to capture entire infrastructure interactions. This study approaches the problem of network interdependence from a more fundamental level. It focuses on network topology, flow patterns within the networks, and optimal interdependent system performance. This approach also allows for probabilistic response characterization of interdependent networked systems when subjected to disturbances of internal nature (e.g., aging, malfunctioning) or disruptions of external nature (e.g., coordinated attacks, seismic hazards). The methods proposed in this study can identify the role that each network element has in maintaining interdependent network connectivity and optimal flow. This information is used in the selection of effective pre-disaster mitigation and post-disaster recovery actions. Results of this research also provide guides for growth of interacting infrastructure networks and reveal new areas for research on interdependent dynamics. Finally, the algorithmic structure of the proposed methods suggests straightforward implementation of interdependent analysis in advanced computer software applications for multi-hazard loss estimation.