  Graphs and complex networks can be successively separated into connected
components associated to respective seed nodes, therefore establishing a
respective hierarchical organization. In the present work, we study the
properties of the hierarchical structure implied by distance-based cutting of
Erd\H{o}s-R\'enyi, Barab\'asi-Albert, and a specific geometric network. Two
main situations are considered regarding the choice of the seeds:
non-preferential and preferential to the respective node degree. Among the
obtained findings, we have the tendency of geometrical networks yielding more
balanced pairs of connected components along the network progressive
separation, presenting little chaining effects, followed by the
Erd\H{o}s-R\'enyi and Barab\'asi-Albert types of networks. The choice of seeds
preferential to the node degree tended to enhance the balance of the connected
components in the case of the geometrical networks.
