The World Wide Web has become part of our everyday life and information retrieval and data mining on the Web are now of enormous practical interest. The algorithms supporting these activities combine the view of the Web as a text repository and as a graph, induced in various ways by links among pages, links among hosts, or other similar networks. The aim of the 4th Workshop on Algorithms and Models for the Web-Graph (WAW 2006)wasto further the understanding of these Web-induced graphsand stimulate the developmentofhigh-performancealgorithmsandapplicationsthat use the graph structure of the Web. The workshop was meant both to foster an exchange of ideas among the diverse set of researchers already involved in this topic and to act as an introduction for the larger community to the state of the art in this area. The workshop program included invited keynote talks by Fan Chung-Graham (UCSD), Soumen Chakrabarti (IITB), Walter Willinger (ATT Research) and Filippo Menczer (Indiana). WAW 2006tookplaceonNovember30 andDecember 1 at the Ban?Inter- tionalResearchInstitute(BIRS),inBan?,Alberta(Canada).Itwasthefourthin a seriesof verysuccessful workshopson the Web graph.WAW 2002 (Vancouver) and 2004 (Rome) were held in conjunction with the Annual IEEE Symposium on Foundations of Computer Science (FOCS). WAW 2003 (Budapest) was held in conjunction with the 12th International World Wide Web Conference.