Subgraphs are one way to focus on parts of a graph.  Another way is to consider <b>path</b>s along consecutive links in a graph.  Fig 1.1s shows a chain of arrows that represent a directed path of <b>A</b> to <b>B</b>



 Fig 1.1s shows a ugraph. It represents unmarked rooms and corridors in a large house.  The room marked <b>A</b> is also the entrance to the house.    A treasure is located in a distant room marked <b>B</b>. 
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An obvious task is to find a way from  <b>A</b> to <b>B</b>  To present some ideas in graph theory in an intuitive manner two attempts to find that way will be presented now.  
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The first attempt is made by a small child who enters the house at room <b>A</b> and wanders about the house through its rooms and corridors hoping to reach some delicious candy room <b>B</b>.  The erratic wanderings can be traced by placing arrows (arcs) along corridors through which the child has gone.  (Assume the child goes completely through a corridor, and not stop or turn around midway.)  An unlucky child may never arrive at room <b>B</b> if he goes through the same rooms and corridors again and again as indicated in Fig 1.1t.
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The second attempt is made by an adult who enters the house at <b>A</b> and searches for the gold left in room <b>B</b>.  He realizes the problem of repeatedly visiting the same rooms (not <b>B</b>).  To avoid visiting the same room he rips up some paper and leaves a piece in each room while in that room.  As he wanders about the house he looks down corridors and does not go through a corridor that leads to a room with paper in it.