285 Copyright © 2019, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 12 DOI: 10.4018/978-1-5225-7570-2.ch012 ABSTRACT The next generation of mobile wireless communications represents a heterogeneous environment which integrates variety of network generation like third generation (3G), fourth generation (4G), and ffth generation (5G). The major challenge in this heterogeneous environment is to decide which access point to use when multiple networks are available. Process of roaming mobile user from one technology to anther diferent is called vertical handover. In this chapter, the authors propose a new mechanism based on graph theory and cost function in order to determine the best path for the end user in terms of qual- ity of service (QoS) when the vertical handover process is needed. Then, they investigate the impact of some existing weighting methods in order to determine the suitable method which can be coupled with the cost function. The experiments evaluation by using Mininet emulator demonstrate that the proposed approach can achieve a signifcant improvement concerning four QoS metrics: throughput, packet lost, packet delay, and packer jitter for two services FTP and video streaming. An Improved Modeling for Network Selection Based on Graph Theory and Cost Function in Heterogeneous Wireless Systems Mohamed Lahby University Hassan II of Casabalanca, Morocco Ayoub Essouiri University Hassan II of Casabalanca, Morocco Abderrahim Sekkaki University Hassan II of Casabalanca, Morocco