In this paper, a graph and matrix theory-based network selection scheme is proposed for overlapping wireless networks which comprises of WiFi/WiMAX/LTE technologies. The parameters data rate, service cost, delay, and power consumption have been taken into account. A graph and corresponding matrix is constructed by considering the above parameters and their relative importance for a particular application. Then, a ‘network satisfaction value’ is determined by computing the permanent of matrix. This value is used to select the optimal access point. In comparison to conventional received signal strength indicator (RSSI) based schemes, improved results have been obtained owing to the proposed graph-based selection mechanism. The results are also compared with those of other existing schemes like TOPSIS (techniques for order preference by similarity to ideal solution), result shows that the proposed scheme is able to select most suitable network according to user preferences, and also reduce the number of handoffs.