If $A$ is the adjacency matrix of the simple graph $G$ with vertex set $V=\{1,2,\ldots,n\}$, then the entry $A_{i,j}$, with $i,j \in V$ is . equal to $0$ exactly when $i$ is not connected to $j$ . equal to $1$ exactly when $i$ is not connected to $j$ . equal to the degree of vertex $i$ . equal to $1$ exactly when there is a path that connect $i$ to $j$. .