A graph and the matrix representing the connection relationships between each vertex of the graph are as follows. What is the value of $a + b + c + d + e$?
A B C D E
$$\left( \begin{array} { l l l l l } 0 & 1 & 1 & 0 & a \\ 1 & 0 & 1 & b & 1 \\ 1 & 1 & c & 1 & 0 \\ 0 & d & 1 & 0 & 1 \\ e & 1 & 0 & 1 & 0 \end{array} \right)$$
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5