Level structure

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{{ safesubst:#invoke:Unsubst||$N=Unreferenced |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} In the mathematical subfield of graph theory a level structure of a graph is a partition of the set of vertices into equivalence classes of vertices with the same distance from a given root vertex.


Given a connected graph G=(V,E) with V the set of vertices and E the set of edges with

the eccentricity of a vertex, for a given vertex v

The partition


is called a level structure of G with root v and depth ε(v).