Cross-file mathjax reference: \ref{blatzo}
We might rightly begin an exploration of graph theory with topics grouped together with a common theme of connectivity.
There is often considerable confusion about these terms. Consider the following definition.
Definition 1 A walk in a graph is a sequence of vertices such that consecutive vertices in the sequence are adjacent in the graph.
Theorem 1 Suppose that \(A\) is the adjacency matrix of a graph, then the number of walks in the graph of length \(k\), between vertices \(v_i\) and \(v_j\) is the \((i,j)\) entry of \(A^k\).
So this definition does not preclude visiting
a vertex more than once, nor going back-and-forth along a single edge.
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