Fig. 3.

The relationship between friendship probability and geographic distance. (A) For each distance δ, the proportion P(δ) of friendships among all pairs u, v of LiveJournal users with d(u, v) = δ is shown. Distances are rounded down to multiples of 10 km. The number of pairs u, v with d(u, v) = δ is estimated by computing the distance between 10,000 randomly chosen pairs of people in the network. The curved line corresponding to P(δ) ∝ ε + 1/δ in A models the fact that some LiveJournal friendships are independent of geography: for distances larger than ≈1,000 km, the background friendship probability ε begins to dominate geography-based friendships. (B) The same data are plotted, correcting for the background friendship probability: we plot distance δ versus P(δ) – 5.0 × 10^–6.