What is the degree sequence of the given HyperGraph, in non-increasing order? V = {v1,v2,v3,v4,v5,v6}E = {{v1,v4,v3} {v2,v3,v6,v5} {v6} {v2} {v1,v5}}
Question
What is the degree sequence of the given HyperGraph, in non-increasing order?
V = {v1,v2,v3,v4,v5,v6}
E = {{v1,v4,v3} {v2,v3,v6,v5} {v6} {v2} {v1,v5}}
Solution
The degree of a vertex in a hypergraph is the number of hyperedges that contain it. So, let's calculate the degree for each vertex:
- v1 is in the hyperedges {v1,v4,v3} and {v1,v5}, so its degree is 2.
- v2 is in the hyperedges {v2,v3,v6,v5} and {v2}, so its degree is 2.
- v3 is in the hyperedges {v1,v4,v3} and {v2,v3,v6,v5}, so its degree is 2.
- v4 is in the hyperedge {v1,v4,v3}, so its degree is 1.
- v5 is in the hyperedges {v2,v3,v6,v5} and {v1,v5}, so its degree is 2.
- v6 is in the hyperedges {v2,v3,v6,v5} and {v6}, so its degree is 2.
So, the degree sequence of the given HyperGraph, in non-increasing order, is: 2, 2, 2, 2, 2, 1.
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