Regarding complex networks, one of the most relevant problems is to understand and to explore community structure. In particular it is important to define the network organization and the functions associated to the different network partitions. In this context, the idea is to consider some new approaches based on interval data in order to represent the different relevant network components as communities. The method is also useful to represent the network community structure, especially the network hierarchical structure. The application of the methodologies is based on the Italian interlocking directorship network.