Quantifying binding specificity and drug resistance of protein kinase inhibitors is of fundamental importance and remains highly challenging due to complex interplay of structural and thermodynamic factors. In this work, molecular simulations and computational alanine scanning are combined with the network-based approaches to characterize molecular determinants underlying binding specificities of the ABL kinase inhibitors. The proposed theoretical framework unveiled a relationship between ligand binding and inhibitor-mediated changes in the residue interaction networks. By using topological parameters, we have described the organization of the residue interaction networks and networks of coevolving residues in the ABL kinase structures. This analysis has shown that functionally critical regulatory residues can simultaneously embody strong coevolutionary signal and high network centrality with a propensity to be energetic hot spots for drug binding. We have found that selective (Nilotinib) and promiscuous (Bosutinib, Dasatinib) kinase inhibitors can use their energetic hot spots to differentially modulate stability of the residue interaction networks, thus inhibiting or promoting conformational equilibrium between inactive and active states. According to our results, Nilotinib binding may induce a significant network-bridging effect and enhance centrality of the hot spot residues that stabilize structural environment favored by the specific kinase form. In contrast, Bosutinib and Dasatinib can incur modest changes in the residue interaction network in which ligand binding is primarily coupled only with the identity of the gate-keeper residue. These factors may promote structural adaptability of the active kinase states in binding with these promiscuous inhibitors. Our results have related ligand-induced changes in the residue interaction networks with drug resistance effects, showing that network robustness may be compromised by targeted mutations of key mediating residues. This study has outlined mechanisms by which inhibitor binding could modulate resilience and efficiency of allosteric interactions in the kinase structures, while preserving structural topology required for catalytic activity and regulation.