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This paper presents a method to assess the state of convergence of Ant Colony Optimization algorithms (ACO) using network science metrics. ACO is a computational intelligence technique inspired by the behavior of ants in nature, and it is commonly used to solve combinatorial optimization problems. In the ACO, artificial ants seek for solutions to the tackled problem, transversing the graph that represents the combinatorial problem. For each displacement, the ants deposit pheromone on the edges which they passed. The ants use the pheromone for indirect communication, and the amount of pheromone weighs the intensity of interaction between the ants. The graph of pheromones forms a network that evolves along the iterations. Network Science allows studying the structure and the dynamics of networks. This area of study provides metrics used to extract global information from networks in a particular moment. This paper aims to show that two network science metrics, the Clustering coefficient, and the Assortativity, can be adapted and used to assess the pheromone graph and extract information to identify the convergence state of the ACO. We analyze the convergence of the four variations of the ACO in the Traveling Salesman Problem (TSP). Based on the obtained results, we demonstrate that it is possible to evaluate the convergence of the ACO for the TSP based on the proposed metrics, especially the adapted clustering coefficient. [ABSTRACT FROM AUTHOR]