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Guilherme Mazui

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What is the Difference Between Walk and Path?

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The main differences between walks and paths in graph theory are as follows:

  • Walk: A walk consists of an alternating sequence of vertices and edges, where consecutive elements are incident, and it begins and ends with a vertex. Walks can have repeated vertices and edges. A walk is an open walk if the starting and ending vertices are different, and it is a closed walk if the starting and ending vertices are the same.
  • Path: A path is a walk without repeated vertices. It is also an open walk, meaning it does not repeat a vertex or an edge. A path with no repeated edges is called a trail. A path is equivalent to a trail with no repeated vertices.

In summary:

  • Walks can have repeated vertices and edges, and they can be open or closed.
  • Paths do not repeat vertices, and they can be open.
  • Trails do not repeat edges, and they are open walks.
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  • What is the Difference Between Walk and Path?
  • Comparative Table: Walk vs Path

    • Comparative Table: Walk vs Path

    The difference between a walk and a path can be summarized as follows:

    Walk Path
    A walk is a finite sequence of alternating vertices and edges, where each edge's endpoints are the two vertices adjacent to it. A path is a walk in which all vertices are distinct, meaning no vertex is repeated.
    A walk can be open (first and last vertex are not equal) or closed (first and last vertex are equal). A path is always simple, meaning it does not repeat any vertices.
    A walk may contain repeated edges. A path does not repeat any edges.
    In a walk, vertices and edges may be traversed multiple times. In a path, vertices are visited only once, but edges may be traversed multiple times.

    In graph theory, a walk is a sequence of edges and vertices, while a path is a specific type of walk where all vertices are distinct and visited only once.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.