MTH 221 Week 4 DQ 3 (UOP Course)

# MTH 221 Week 4 DQ 3 (UOP Course)

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Week 4 DQ3

Random graphs are a fascinating subject of applied and theoretical research. These can be generated with a fixed vertex set V and edges added to the edge set E based on some probability model, such as a coin flip. Speculate on how many connected components a random graph might have if the likelihood of an edge (v1,v2) being in the set E is 50%. Do you think the number of components would depend on the size of the vertex set V? Explain why or why not.

The total number of possible edges between vertices is C(n,2). So for 4 vertices, it's 6 possible edges. For 100 vertices, it's 4950 possible edges.

Per definition 11.5 on page 517 of the text, a component of a graph is a subgraph.

This problem presents a type of random graph described...

MTH 221
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Excerpt from file: Week4DQ3 Randomgraphsareafascinatingsubjectofappliedandtheoreticalresearch.Thesecanbe generatedwithafixedvertexsetVandedgesaddedtotheedgesetEbasedonsome probabilitymodel,suchasacoinflip.Speculateonhowmanyconnectedcomponentsa randomgraphmighthaveifthelikelihoodofanedge(v1,v2)beinginthesetEis50%.Do...

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