The methods to evaluate the robustness of a network have been extensively studied. Such methods often require obtaining traffic equilibrium conditions or solving mathematical problems, and these methods can only be applied to a network of limited size. On the other hand, nowadays detail road network data can be downloaded freely, and such data may provide different insights on network robustness evaluation. This paper applies the capacity-weighted eigenvector centrality method to identify the strongly and weakly connected parts of large networks. The eigenvector centrality is one of the evaluation methods based on network topology with a small computational load. This method can be applied to directed networks and does not require their adjacency matrices to be symmetric. Several numerical examples showed that the capacity-weighted eigenvector centrality analysis can identify the strongly and weakly connected parts of the network, and it can be used to evaluate connectivity of network for robustness.