An algebraic framework of weighted directed graphs
Summary: We show that an algebraic formulation of weighted directed graphs leads to introducing a \(k\)-vector space equipped with two coproducts \(\Delta\) and \(\widetilde{\Delta}\) verifying the so-called coassociativity breaking equation \((\widetilde{\Delta} \otimes \text{id})\Delta = (\text{id} \otimes \Delta)\widetilde{\Delta}\). 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.
scientific article; zbMATH DE number 2012638