Question

Given a graph, say

g = Graph[{x -> a, y -> c, a -> b,
           b -> c, a -> c, d -> c,
           a -> d, b -> d},
      VertexLabels -> "Name"] 

How do I find all vertices in a graph with the maximum degree i.e. a list of all vertices that has the most number of edges, and highlight them in the graph?

In this case, it would be the vertices {a,c}.

Answer 1

Here’s an approach using DegreeCentrality:

(* In[41]:= *) max = Pick[VertexList[g], DegreeCentrality[g], Max[DegreeCentrality[g]]]

(* Out[41]= *) {a, c}

(* In[42]:= *) HighlightGraph[g, max]