Check if graph is multigraph given degree sequence

Question

I am given some degree sequences of graphs, and my question is what is the method to determine which of them are sequences corresponding to multigraphs.

1. 1,2,2,3
2. 0,1,2,3
3. 2,2,2,2

Answer 1

They're all realizable for multigraphs; with 4 vertices, you can just try by hand:

We also see that $(1,2,2,3)$ and $(2,2,2,2)$ are realizable for simple graphs.

However, the sequence $(3,2,1,0)$ is not realizable for simple graphs: the vertex of degree 3 needs to attach to 3 other vertices, but there are only 3 other vertices and one has degree 0 (i.e., no edges).