This book constitutes the proceedings of the 18th International Workshop on Algorithms and Models for the Web Graph, WAW 2023, held in Toronto, Canada, in May 23-26, 2023.The 12 Papers presented in this volume were carefully reviewed and selected from 21 submissions. The aim of the workshop was understanding of graphs that arise from the Web and various user activities on the Web, and stimulate the development of high-performance algorithms and applications that exploit these graphs.