I had to draw a simple graph (undirected, no multiple edges & loops) and the degrees of the vertices were $1, 1, 2, 3, 4, 5, 6$.
I knew the total degree was an even number $(22)$, so the graph must exist. I tried drawing $6$ edges from the highest-degree vertices $(6)$, then chose a random vertex and drew $4$ edges from there (because it already has $1$ edge). I kept doing this for a while and ultimately the graph had $2$ vertices of degree $2$, which was not what I wanted.
Is there a method for drawing simple graphs given the degrees of the graph's vertices?