Before revision:  In this paper, first we discuss that these two modes can be associated with a category theoretic duality (adjunction) and derive a natural network structure (a path notion) for each mode by appealing to a category theoretic universality.
After revision:  In this paper, first we discuss that these two modes can be associated with a category theoretic duality (adjunction) and derive a natural network structure (a path notion) for each mode by appealing to the category theoretic universality.