Indication of long-range correlations governing city size

City systems are characterized by the functional organization of cities on a regional or country scale. While there is a relatively good empirical and theoretical understanding of city size distributions, insights about their spatial organization remain on a conceptual level. Here we analyze empirically the correlations between the sizes of cities (in terms of area) across long distances. Therefore, we (i) define city clusters, (ii) obtain the neighborhood network from Voronoi cells, and (iii) apply a fluctuation analysis along all shortest paths. We find that most European countries exhibit long-range correlations but in several cases these are anti-correlations. In an analogous way we study a model inspired by Central Places Theory and find that it leads to positive long-range correlations, unless there is strong additional spatial disorder – contrary to intuition. We conclude that the interactions between cities extend over large distances reaching the country scale. Our findings have policy relevance as urban development or decline can affect cities at a considerable distance.