There are a few concepts within graph theory that include walks, paths, trails and cycles. A walk on a graph is defined as a sequence of adjacent vertices where repetition is allowed. A path is a walk, however, no vertices can be repeated in this case. Within Notice that within  these two concepts, it is known that if a walk exists between  between   class="ltx_Math" contenteditable="false" data-equation="x">\(x\) and  data-equation="x">\(x\) and   class="ltx_Math" contenteditable="false" data-equation="y">\(y\), then a path also exists from  from   class="ltx_Math" contenteditable="false" data-equation="x">\(x\) to  data-equation="x">\(x\) to   class="ltx_Math" contenteditable="false" data-equation="y.">\(y.\)