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graphs 20

# graphs 20 - Graphs Why Graphs Graphs provide a model for...

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Graphs

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Graphs 2 Why Graphs? Graphs provide a model for many real world problems…such as: Topological Sorting This is the process of arranging the vertices of a graph into a linear order. Minimum Spanning Trees A spanning tree is a subgraph of a connected undirected graph that contains all of the graph’s vertices and enough of its edges to form a tree. In a minimum spanning tree, the edges are weighted, and the goal is to create a spanning tree with a minimum sum of weighted edges. Shortest Paths Circuit Design
Graphs 3 Terms A graph is a collection of vertices or nodes, pairs of which are joined by lines called edges . This definition is often expressed as: G = (V,E) where V and E are finite sets. The elements in V are called vertices . The elements in E are called edges and are represented as a tuple (i,j) where i and j are 2 vertices contained in V. Graphs are usually displayed as diagrams with circles denoting vertices and lines representing edges. An edge may be either directed or undirected . Directed edges are represented by an arrowhead and are not symmetric. Edge (i, j) is oriented from i to j and is not the same as Edge (j,i) which is oriented j to i.

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Graphs 4 An undirected graph contains only undirected edges. There can be at most 1 edge between any pair of vertices. A
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graphs 20 - Graphs Why Graphs Graphs provide a model for...

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