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# Strongly connected if each node can reach every other

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Unformatted text preview: is connected (i.e., ignoring the directions of edges). strongly connected if each node can reach every other node by a “directed path”. 1 2 3 Figure: A directed graph that is connected but not strongly connected 10 Networks: Lecture 2 Graphs Trees, Stars, Rings, Complete and Bipartite Graphs A tree is a connected (undirected) graph with no cycles. A connected graph is a tree if and only if it has n − 1 edges. In a tree, there is a unique path between any two nodes. Complete graph Ring Star Bipartite graph Tree actors movies 11 Networks: Lecture 2 Graphs Neighborhood and Degree of a Node The neighborhood of node i is the set of nodes that i is connected to. For undirected graphs: The degree of node i is the number of edges that involve i (i.e., cardinality of his neighborhood). For directed graphs: Node i ’s in-degree is ∑j gji . Node i ’s out-degree is ∑j gij . 1 2 4 3 Figure: Node 1 has in-degree 1 and out-degree 2 12 Networks: Lecture 2 Properties of Networks Properties of Networks While a small network can be visualized directly by its graph (N , g ), larger ne...
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