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# E with minimum number of edges between these nodes a

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Unformatted text preview: geodesic between nodes i and j is a “shortest path” (i.e., with minimum number of edges) between these nodes. A path is a walk where there are no repeated nodes. The length of a walk (or a path) is the number of edges on that walk (or path). For directed graphs, the same deﬁnitions hold with directed edges (in which case we say “a path from node i to node j ”). 8 Networks: Lecture 2 Graphs Walks, Paths, and Cycles—2 j i walk i j path between i and j j i i cycle j shortest path Note: Under the convention gii = 0, the matrix g 2 tells us number of walks of length 2 between any two nodes: (g × g )ij = ∑k gik gkj Similarly, g k tells us number of walks of length k . 9 Networks: Lecture 2 Graphs Connectivity and Components An undirected graph is connected if every two nodes in the network are connected by some path in the network. Components of a graph (or network) are the distinct maximally connected subgraphs. A directed graph is connected if the underlying undirected graph...
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