3 ms·
Could you elaborate ?
by PartiallyTyped 2y ago
Could you elaborate ?
- ororroro 2y agoI am not an expert but it looks like the quanta author has invented a definition for "highly connected" because C-expander was too complicated a concept for them (me too). There are older competing definitions for "highly connected" along the lines of a graph where the number of edges is greater then half the number of vertices which is obviously insufficient to guarantee a loop. Then they have used networks instead of graphs and added a comma, for no apparent reason.
- noqc 2y agoSure, a graph is connected if it has a spanning tree, which requires |E|>=|V|-1. Presumably a graph is only highly connected if it has more edges than this minimal requirement, so we have |E|>=|V|, and this graph must have a loop.