An algebraic framework of weighted directed graphs
Philippe Leroux1
Received19 Feb 2003
Abstract
We show that an algebraic formulation of weighted directed graphs
leads to introducing a k-vector space equipped with two
coproducts Δ and Δ˜ verifying the so-called
coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is
called an L-coalgebra. Explicit examples of such
spaces are constructed and links between graph theory and
coassociative coalgebras are given.