We defined and developed a computational procedure for finding the intermediary nodes in networks we named Noeuds de liaison. A noeud de liaison refers to any cut-vertex v of a graph G but is not a member of any pseudo-clique Qi, ∀ Qi ⊆ G. The pseudo-clique Q is made up of nodes in G that are closely connected to each other, and where the nodes form at least a ring C and at most a complete graph K. The computational procedure took O(V+E) to print out all the noeuds de liaison. Our major finding is that we designed a linear time algorithm and wrote a computer program for computing all the noeuds de liaison in undirected graphs.