I 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 the

I 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.