Graphs

# Graphs - Graphs Graphs Network Example 1 Web graph Each...

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Graphs Graphs -- Network Example 1 - Web graph Each vertex is a web page Each edge is one or more links from a page to another Directed graph - all edges have direction e.g. street map, pre-req graph (on Rutgers CS website) Neighbors of a vertex y is a neighbor of x if edge, y is adjacent to x o neighbor = adjacent (x) -> (y) o x is not a neighbor of y, not adjacent to y Path from x to y is sequence of edges without repetition p1 -> p2 (simple edge is a path) p4 -> p6 -> p4 is a path, actually a cycle o cycle is a path with the same start and end points o p3 -> p5 -> p6 -> p3 = (p3, p5, p6, p3) indegree - number of edges into a vertex for p6, indegree = 2 outdegree - number of edges out of p6 for p6, indegree = 2 Degree - int + out = 4 Facebook graph is undirected ‘symmetric’ relationship o e.g. friendship on facebook (p1, p3) in an undirected graph: o p1 is adjacent to p3, and vice versa Directed - ALL edges have direction Undirected - NO edge has direction Cliques - group within a graph Can have weights at the edges - edge “weight” e.g. distance in a street graph e.g. molecules bonds o undirected, weights would be bond strength (double bond, triple bond)

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In summary directed, no weights undirected, no weights directed, weighted
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Graphs - Graphs Graphs Network Example 1 Web graph Each...

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