This paper presents a model and analytical framework for studying interdependent networks, where the failure of nodes in one network can cause failures in another network, leading to cascading failures. The study shows that for two interdependent Erdos-Renyi (ER) networks, the critical average degree below which both networks collapse is 2.445, compared to 1 for a single ER network. This indicates that interdependent networks are more vulnerable to random failures than single networks, even though a broader degree distribution is typically more robust for single networks. The model considers two networks, A and B, where nodes in one network depend on nodes in the other network. The failure of nodes in one network can cause failures in the other, leading to a cascade of failures. The study uses percolation theory and generating functions to analyze the critical fraction of nodes that must be removed to cause complete fragmentation of all networks. For ER networks, the critical fraction of nodes that must be removed to cause complete fragmentation is found to be 2.445, which is significantly higher than the 1 for a single ER network. This suggests that interdependent networks require a higher level of robustness to avoid complete fragmentation. The study also shows that for scale-free networks, the critical fraction of nodes that must be removed to cause complete fragmentation remains finite even for degree distributions with λ > 2, which is different from the behavior of regular percolation in such networks. The results show that interdependent networks are more vulnerable to random failures than single networks, even though a broader degree distribution is typically more robust for single networks. This is because the dependencies between networks can cause the failure of high-degree nodes to have a more significant impact on the overall network. The study also highlights the importance of considering interdependencies when designing robust networks, as current methods may not account for these dependencies. The findings have important implications for the design of robust real-world networks, as they show that interdependent networks require a different approach to ensure robustness.This paper presents a model and analytical framework for studying interdependent networks, where the failure of nodes in one network can cause failures in another network, leading to cascading failures. The study shows that for two interdependent Erdos-Renyi (ER) networks, the critical average degree below which both networks collapse is 2.445, compared to 1 for a single ER network. This indicates that interdependent networks are more vulnerable to random failures than single networks, even though a broader degree distribution is typically more robust for single networks. The model considers two networks, A and B, where nodes in one network depend on nodes in the other network. The failure of nodes in one network can cause failures in the other, leading to a cascade of failures. The study uses percolation theory and generating functions to analyze the critical fraction of nodes that must be removed to cause complete fragmentation of all networks. For ER networks, the critical fraction of nodes that must be removed to cause complete fragmentation is found to be 2.445, which is significantly higher than the 1 for a single ER network. This suggests that interdependent networks require a higher level of robustness to avoid complete fragmentation. The study also shows that for scale-free networks, the critical fraction of nodes that must be removed to cause complete fragmentation remains finite even for degree distributions with λ > 2, which is different from the behavior of regular percolation in such networks. The results show that interdependent networks are more vulnerable to random failures than single networks, even though a broader degree distribution is typically more robust for single networks. This is because the dependencies between networks can cause the failure of high-degree nodes to have a more significant impact on the overall network. The study also highlights the importance of considering interdependencies when designing robust networks, as current methods may not account for these dependencies. The findings have important implications for the design of robust real-world networks, as they show that interdependent networks require a different approach to ensure robustness.