Find an Eulerian path or circuit in a graph given its adjacency matrix

Question

Consider the graph with adjacency matrix \begin{pmatrix} 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \end{pmatrix}

Can you find an Eulerian path or circuit in this graph? What is it?

Answer 1

I'll make my comment an answer/hint if just to reduce the unanswered queue by $\epsilon$.

Hint: From the adjacency matrix, you can see that the graph is $3$-regular. In particular, there are at least $3$ vertices of odd degree.