In cognitive radio networks, signal to interference plus noise ratio (SINR) is a quantity that is used to analyze the bounds of the capacity of a channel. This is the reason for SINR being one of the important parameters toward evaluating the performance of spectrum sharing in every network. To maximize the channel utilization in any network, the SINR of a channel should be considered to be within a threshold. This also leads to lesser power consumption, and the quality of service for the licensed users is maintained. Further, reduced SINR leads to an improvement in the quality of communication in the network. In this paper, a graph theoretic measure for the efficient utilization of channels in cognitive radio networks has been proposed and is named as channel criticality based resource allocation (CCRA). Using the SINR as the weight of the graph, a novel concept of channel criticality has also been introduced in this work. The proposed CCRA technique has also been compared with the existing interference aware channel assignment (IACA) technique in terms of the channel utilization. Through simulations, the CCRA has been observed to outperform the IACA scheme. The average channel utilization of the proposed CCRA was observed to have increased by 8%, when the secondary users were introduced in the network as compared with the IACA technique. Copyright Int. J. Commun. Syst. 2017; 30: e3012 V. KUMAR AND S. MINZThe betweenness of the link k for the source and destination pair .a; b/ is given by of 12 6