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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 Fall '09
 Acemoglu
 Graph Theory, Graph Theory and Social Networks

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