While trying yEd, I opted for the "Java" version, as I already have a java installed.
Sure enough, it contains a .jar file with (presumably) all required files, but there is no indication (at least I couldn't find it) as to how to start the jar.
"java -jar yed.jar" is guessable, but that does not run, as it needs a main class as well to start, which is not mentioned anywhere.