A Weighted Quiver Kernel using Functor Homology

In many applications, vertices or edges of graphs and quivers are labeled and have costs associated with them, also called weights. In this paper, we are interested in edge-weighted quivers. These weights are not restricted to just scalar values, but can also represent much more complex and richer relations between the nodes of an edge by modeling them as label sets or a function of several variables. Such weighted quivers arise frequently when modeling real-world applications, especially where the relationships among objects play an important role. Below are a few applications of weighted quivers that cover wide and diverse fields: - Physics: weighted quivers are used to represent atomic structures, where an atom is depicted as a vertex and the interactive forces between the atoms (i.e., vertices) are shown as directed edges between pairs of vertices. The edge weights here can model the strength of interaction between two vertices. Note that such a weighted quiver also accepts multiple edges between the same pair of vertices, where each edge potentially represents a different type of interactive force.