Table 2 Definition of the metrics characterising the activity space and the social circle. (1) The size of a set is the number of elements in the set. (2) We compute the entropy of a set considering the probability \(p(j)\) associated to each element j of the set. (3) We measure the stability \(J_{\mathrm{AS}}\) by computing the Jaccard similarity between the activity space at t and at \(t-T\), with \(T=20\) weeks. \(J_{\mathrm{SC}}\) is computed in the same way for the social circle. (4) We compute the rank turnover of a set by measuring for each of its elements j the absolute change in rank between two consecutive time windows of length \(T=20\) weeks. The rank is attributed based on the probability \(p(j)\). The average absolute change in rank across all elements corresponds to the rank turnover

(1) Size

\(\displaystyle C(i,t) = |AS_{i}(t)|\)

k(i,t)=|SC(i,t)|

(2) Entropy

\(\displaystyle H_{\mathrm{AS}} (i,t) = -\sum_{j=1}^{C(i,t)}{p(j) \log p(j)}\)

\(\displaystyle H_{\mathrm{SC}}(i,t) = -\sum_{j=1}^{k(i,t)}{p(j) \log p(j)}\)

(3) Stability

\(\displaystyle J_{\mathrm{SC}}(i,t)=\frac{|SC(i,t)\cap SC(i,t-T)|}{|SC(i,t)\cup SC(i,t-T)|}\) ^∗

\(\displaystyle J_{\mathrm{AS}}(i,t)=\frac{|AS(i,t)\cap AS(i,t-T)|}{|AS(i,t)\cup AS(i,t-T)|}\) ^∗

(4) Rank turnover

\(\displaystyle R_{\mathrm{AS}}(i,t)=\sum_{j=1}^{N}\frac{|r(j,t) - r(j, t- T)|}{N}\) ^†

\(\displaystyle R_{\mathrm{SC}}(i,t)=\sum_{j=1}^{N}\frac{|r(j,t) - r(j, t- T)|}{N}\) ^†