Adequate representation of cartographic expert knowledge is essential if maps are to be created in an automated way. Part of this expert knowledge is made up by the structural knowledge embedded in the relations that exist among the objects depicted on a map, as these define the structures and patterns of the corresponding real-world objects that should be maintained and emphasized in the cartographic generalization process. With this article we aim to provide a foundation for the analysis and representation of such relations among objects in thematic and topographic maps, which we term horizontal relations. We start off by defining the terminology underlying map object relations and by discussing how these relations interact with map constraints and cartometric measures. We then present a typology of horizontal relations that may be found in a map with respect to map generalization. The typology is the result of a study of thematic and topographic maps, as well as an analysis of the literature on the use of map object relations. Five different types of horizontal relations are identified: geometric, topological, semantic, statistical and structural. Some of these can be based on standard operations available in commercial GIS or mapping systems, while others are less easily accessible. To demonstrate the use of our typology and show how complex horizontal relations can be formalized, we present an application of the typology to the grouping and generalization of islands. Subsequently, we discuss the various steps involved in the usage of horizontal relations in map generalization, as well as their associated roles.