Can I make a simple suggestion: Avoid the words "graph" and "edge" in any public marketing materials. If you must use the words under the hood, so be it.
Here's the problem:
A graph theorist (or probably any computer scientist) hears "graph" and thinks "network."
A normal person (even a well-educated one outside of a couple specific fields) hears "graph" and thinks "chart of data." Calling it a graph will actually mislead most people.
Edge is even worse: A graph theorist hears "edge" and thinks "connection between network nodes."
A normal person hears "edge" and thinks something like "boundary;" such as "the part of my kitchen table where I shouldn't set my drinks." Or even worse, they think "the sharp part of a knife." Calling it an edge will make most people immediately and utterly confused, because in the vernacular, "edge" means something totally different than what you want it to mean.
You are setting up a massive language barrier if you use the word "edge," because it doesn't have any intuitive connection in most peoples' minds to network links.
I'm guessing you call it Key Graph because you think the word "net" is over-used; I'll give you that. But please please please use a word like "link" or "connection" or "keynnection" or anything but "edge."