To capture this, we define the tie strength of each individual i as the highest value of her incident edges.
for all individuals j directly connected to i: Taking the maximum captures what we are after: A community member who only has weak connections will have low tie-strength and be considered a weak-tie user, while a member with either strong connections only or with both strong and weak connections will have high tie-strength and be considered a strong-tie user, who will be part of a local clique (Luce and Perry, 1949).