A graph with $5$ vertices and $7$ edges is shown.

Loop e$1$ connects vertex v$1$ and vertex v$1.$

Edge e$2$ connects vertex v$1$ and vertex v$2.$

Edge e$7$ connects vertex v$1$ and vertex v$3.$

Loop e$3$ connects vertex v$2$ and vertex v$2.$

Edge e$6$ connects vertex v$2$ and vertex v$3.$

Edge e$4$ connects vertex v$2$ and vertex v$5.$

Edge e$5$ connects vertex v$2$ and vertex v$5.$

Vertex v$4$ is isolated. What is the degree of v$2?$