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This is a 2-approximation algorithm. Let the total number of edges in the graph be $E$. Let $n$ be the number of nodes. For every single edge in the graph, it has two nodes. Let's label the first node as the $Start$ node and the other node at the $End$ node.   When the $End$ node gets added to the graph problem, the edge is created. Now let $e_i$ be the number of edges that the node $i$, is considered the $End$ node. Since every single edge has one $End$ node, that means $\sum{i=1}{n} $\sum\limits_{i=1}^n  e_i = E$the sum from i=1 to n of ei=E (which is the total number of edges)