Actually, all the graphs we have seen above are just drawings of graphs. A graph is really an abstract mathematical object consisting of two sets \(V\) and \(E\) where \(E\) is a set of 2-element subsets of \(V\text{.}\) Are the graphs below the same or different?
\(V = \{a, b, c, d, e\}\text{,}\)
\(E = \{\{a,b\}, \{a, c\}, \{a,d\}, \{a,e\}, \{b,c\}, \{d,e\}\}\text{.}\)
\(V = \{v_1, v_2, v_3, v_4, v_5\}\text{,}\)
\(E = \{\{v_1, v_3\}, \{v_1, v_5\}, \{v_2, v_4\}, \{v_2, v_5\}, \{v_3, v_5\}, \{v_4, v_5\}\}\text{.}\)