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.

I'm going to start with a few preliminaries:

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

jacob

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

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