Networked systems can be represented using graphs.
Tenants who use the systems in which their resources are
hosted need to check with the provider of the resources that
their resources are properly connected and that
their resources are properly separated from the resources of
other tenants. Since providers manage systems for
multiple tenants, a method to prove the connectivity and isolation
without revealing the network topology is required. As a solution,
an efficient zero-knowledge proof system of graph signatures
using a bilinear-map accumulator has been proposed, where the
verification time and the size of the proof data do not depend on
the number of graph vertexes and edges. However, this system
has two problems. First, since the proof does not include labels,
it is not possible to prove the connectivity considering network
bandwidth and cost. Second, since it assumes undirected graphs,
it cannot handle applications on directed graphs such as network
flows. In this study, we extend the previous system and propose
a zero-knowledge proof system of the connectivity for directed
graphs where each edge has labels. We implemented our system
on a PC using a pairng library and evaluate it by measuring the
processing times.