Graph Theory By Narsingh Deo Exercise Solution [extra Quality] (TRUSTED ✭)

Therefore: $$ \sum_i=1^n deg(v_i) = 2 \times |E| $$

Trees, Spanning Trees, Fundamental Circuits, and Distance. Graph Theory By Narsingh Deo Exercise Solution

Proof: Let $G = (V, E)$ be a graph with $n$ vertices and $e$ edges. Every edge in a graph connects two vertices (or a vertex to itself in a loop). Therefore, every edge contributes 2 to the total sum of degrees. Therefore: $$ \sum_i=1^n deg(v_i) = 2 \times |E|