Geographical Variability as a Determinant of Large-scale Network Structure∗

It is a well-established result that the marginal probability of a social tie between two persons declines with geographical distance for a wide range of social relations (see, e.g., Bossard, 1932; Zipf, 1949; Festinger et al., 1950; Hägerstrand, 1967; Freeman et al., 1988; Latané et al., 1995; McPherson et al., 2001). While often regarded as a mere curiosity, others have argued that this relationship is a critical determinant of social structure (Mayhew, 1984). Indeed, Butts (2003) has shown that under fairly weak conditions, spatial structure is adequate to account for the vast majority of network structure (in terms of total entropy) at large geographical scales.