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The medial graph of any plane graph is a 4-regular plane graph. For any plane graph G, the medial graph of G and the medial graph of the dual graph of G are isomorphic. Conversely, for any 4-regular plane graph H, the only two plane graphs with medial graph H are dual to each other. [4]
The median of three vertices in a tree, showing the subtree formed by the union of shortest paths between the vertices. Every tree is a median graph. To see this, observe that in a tree, the union of the three shortest paths between pairs of the three vertices a, b, and c is either itself a path, or a subtree formed by three paths meeting at a single central node with degree three.
Medial axis, in geometry the set of all points having more than one closest point on an object's boundary; Medial graph, another graph that represents the adjacencies between edges in the faces of a plane graph; Medial triangle, the triangle whose vertices lie at the midpoints of an enclosing triangle's sides; Polyhedra: Medial deltoidal ...
The original knot diagram is the medial graph of this new plane graph, with the type of each crossing determined by the sign of the corresponding edge. Changing the sign of every edge corresponds to reflecting the knot in a mirror .
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution , from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
The medial graph of the dual graph of a plane graph is the same as the medial graph of the original plane graph. [30] For regular polyhedra or simple polyhedra, the medial graph operation can be represented geometrically by the operation of cutting off each vertex of the polyhedron by a plane through the midpoints of all its incident edges. [31]
The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
A median graph is an undirected graph in which for every three vertices , , and there is a unique vertex ,, that belongs to shortest paths between any two of , , and . If this is the case, then the operation x , y , z {\displaystyle \langle x,y,z\rangle } defines a median algebra having the vertices of the graph as its elements.