When can any weight function be turned into a strictly monotone weight function?
Weighted Directed Graphs in Applications
Artificial Neural Networks
SUMMARY: We define a directed graph as a space with any binary relation, and we define a strictly monotone weight function on any directed graph. We prove when no weight function on a directed graph can be turned into a strictly monotone weight function, and we give a characterization of any strictly monotone weight function. Finally, we mention the use of weighted directed graphs in autonomous driving research, quantum information, and deep learning.
Here is an example of a directed graph:
A directed graph
Other examples are the real numbers with the strict order $<$ and any collection of subsets of any set with the binary relation $\subseteq$ of ``being a subset of''.
You are unauthorized to view this page.