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HEADERS_END

There are two meanings of the word graph in Mathematics

There are two main meanings of the word graph in Mathematics:

(1) A mathematical object consisting of nodes and edges.

* A mathematical object consisting of nodes and edges.

** Such a graph is often represented by a diagram consisting of dots (representing nodes) and lines (representing edges).

A graph is often represented by a diagram consisting of dots (representing nodes) and lines (representing edges).

(2) A diagram illustrating the relationship between two or more variables.

* A diagram illustrating the relationship between two or more variables.

** Such a diagram is often used to draw the graph of a function

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We can define a distance function between vertices /x/ and /y/ of a graph by taking the length of the shortest path from /x/ to /y./ Such a distance function defines a metric on the vertices, and thus we get a metric space.

For a graph in the first sense - points and edges - we can define a distance function between

vertices /x/ and /y/ of a graph by taking the length of the shortest path from /x/ to /y./

Such a distance function defines a metric on the vertices, and thus we get a metric space.

If we put non-negative weights on the edges and define the function /d(x,y)/ to be the minimal

sum of weights taken over all possible paths from /x/ to /y/ we again get a metric space with

the elements being the vertices of the graph.