Fig. 1

Suppose the persons i and j are not currently social contacts in SocNetbut have three different common social contacts k₀,k₁, and k₂ through different activities. They might be connected in the extended social network, ESocNet, when at least one of their common social contacts meet them within the same activity location. Suppose \(A_{ik_0}=A_{jk_0}=A_{ik_1}=A_{jk_1}=A\ne A_{ik_2}\ne A_{ik_2}\), that is, k₀ meets i and j at the same location, similarly k₁ meets i and j at the same location to k₀’s, however, k₂ meets them in different places. To compute \(p^A_i\) and \(p^A_j\) we only count the social contacts who meet them at the same location A, therefore, \(p^A_i=(T^A_{ik_0}+T^A_{ik_1})/{2}\), and \(p^A_j=(T^A_{jk_0}+T^A_{jk_1})/{2}\). Finally, the probability that i and j make an edge- are connected in the extended social network- is \(1-(1-p^A_ip^A_j)^{2}\)