Median Algebra
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High Quality Content by WIKIPEDIA articles! A median graph is an undirected graph in which for every three vertices x, y, and z there is a unique vertex that belongs to shortest paths between any two of x, y, and z. If this is the case, then the operation defines a median algebra having the vertices of the graph as its elements. Conversely, in any median algebra, one may define an interval [x, z] to be the set of elements y such that = y. One may define a graph from a median algebra by creating a vertex for each algebra element and an edge for each pair (x, z) such that the interval [x, z]…mehr

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High Quality Content by WIKIPEDIA articles! A median graph is an undirected graph in which for every three vertices x, y, and z there is a unique vertex that belongs to shortest paths between any two of x, y, and z. If this is the case, then the operation defines a median algebra having the vertices of the graph as its elements. Conversely, in any median algebra, one may define an interval [x, z] to be the set of elements y such that = y. One may define a graph from a median algebra by creating a vertex for each algebra element and an edge for each pair (x, z) such that the interval [x, z] contains no other elements. If the algebra has the property that every interval is finite, then this graph is a median graph, and it accurately represents the algebra in that the median operation defined by shortest paths on the graph coincides with the algebra's original median operation.