Recently, considerable efforts have been made towards building a quantum Internet - an interconnected network of users enabled to perform desired quantum information processing and computing tasks among them. Considering quantum networks, I will discuss practical bottlenecks for secure communication and resource distribution among end nodes in this presentation. Motivated by the power of abstraction in graph theory (in association with quantum information theory), I will present graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over the quantum Internet. Next, considering a particular bipartite network where the end users have constrained free will, I will present limitations on testing quantum nonlocal correlations using such a network and imperfect devices.