Although node-link representations of graphs are widespread and even sometimes preferred to other approaches, they suffer from obvious limitations when graphs become large or dense, inducing visual cluttering and impeding the traditional visual information seeking process. This article presents a new strategy of exploration particularly suitable when graphs are large and dense. Users iteratively drive the exploration through the visualization of small sub-networks of interest. Our technique is particularly useful with multilayer networks, where layers typically combine into a large and dense network. Our iterative exploration process called M-QuBE³ computes a score for each node of a graph based on structural and semantic information where more interesting nodes from a user point of view have higher scores. This in turn translates into a procedure to select sub-networks of interest. Within each sub-network, the user can select nodes to enhance the semantic context (and thus impact their interest score) and iteratively refine the exploration towards more relevant sub-networks. The M-QuBE³ process natively handles multilayer network and allows the use of layers as a semantic apparatus when driving the navigation.