# ChA.4-Connectivity.ppt - Connectivity Jorge A Cobb The...

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1 Connectivity Jorge A. Cobb The University of Texas at Dallas

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2 Paths in graphs A path of length n in an undirected graph is a sequence of n edges such that successive edges share a common endpoint. In a directed graph, each edge in the path (except the first) has as initial vertex the terminal vertex of the previous edge in the path. In a simple graph (i.e., each pair of nodes can have at most one edge between them), a path is a sequence of (pairwise) adjacent vertices.
3 Path examples in a simple undirected graph a,b,c Written differently: (a,b), (b,c) a,d,e,f a ,b,c,d, a, e,b,f d,c,f d,c,f,e,d

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4 The centroid of a graph We define the centroid of a graph as the vertex which minimizes the sum of the lengths of the shortest paths to every other vertex Centroid of this graph?
5 Circuits and simple paths A path is a circuit if it starts and ends in the same vertex and has length greater than zero. A path (or circuit) is simple if no edge appears more than once in it.

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