Philippe Leroux, "An algebraic framework of weighted directed graphs", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 406523, 22 pages, 2003. https://doi.org/10.1155/S0161171203302170
An algebraic framework of weighted directed graphs
We show that an algebraic formulation of weighted directed graphs leads to introducing a -vector space equipped with two coproducts and verifying the so-called coassociativity breaking equation . Such a space is called an -coalgebra. Explicit examples of such spaces are constructed and links between graph theory and coassociative coalgebras are given.
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