The Structure of Borders in a Small World
(a) Multi-scale human mobility is characterized by dominant short range and significant long-range connectivity patterns. The illustrated network represents a proxy for human mobility, the flux of bank notes between 3,109 counties in the lower 48 United States. Each link is represented by a line, the color scale encodes the strength of a connection from small (dark red) to large (bright yellow) values of spanning four orders of magnitude. (b) A simplified illustration of generic traffic patterns between and within metropolitan mobility hubs (A and B), with two types of connections and , local traffic connecting individual hubs to smaller nodes in their local environment (blue) and long distance links connecting the hubs (red). Depending on the ratio of local and long range flux magnitude, two qualitatively different modularizations are plausible. If , two spatially compact communities are meaningful (left), whereas if , the metropolitan centers belong to one yet geographically delocalized module (orange), effectively detached from their local environment, yielding three communities altogether (right). (c) Multi-scale mobility networks are strongly heterogeneous as reflected by the functions , , and , the relative frequencies of distances , link weights and vertex flux that all are distributed over several orders of magnitude.