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For directed graphs e is the set of directed edges ie

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Unformatted text preview: edges in the network. For directed graphs: E is the set of “directed” edges, i.e., (i , j ) ∈ E . For undirected graphs: E is the set of “undirected” edges, i.e., {i , j } ∈ E . In Example 1, Ed = {(1, 2), (2, 3), (3, 1)} � � In Example 2, Eu = {1, 2}, {1, 3}, {2, 3} When are directed/undirected graphs applicable? Citation networks: directed Friendship networks: undirected We will use the terms network and graph interchangeably. We will sometimes use the notation (i , j ) ∈ g (or {i , j } ∈ g ) to denote gij = 1. 7 Networks: Lecture 2 Graphs Walks, Paths, and Cycles—1 We consider “sequences of edges” to capture indirect interactions. For an undirected graph (N , g ): A walk is a sequence of edges {i1 , i2 }, {i2 , i3 }, . . . , {iK −1 , iK }. A path between nodes i and j is a sequence of edges {i1 , i2 }, {i2 , i3 }, . . . , {iK −1 , iK } such that i1 = i and iK = j , and each node in the sequence i1 , . . . , iK is distinct. A cycle is a path with a final edge to the initial node. A...
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This document was uploaded on 03/18/2014 for the course EECS 6.207J at MIT.

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