attack - Random Graphs 858L Descriptive Studies of...

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Random Graphs 858L
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Descriptive Studies of Biological Graphs What to networks that arise in nature “look like”? What are their characteristics? Related to random graphs because you need to know what features can arise just by chance. Need to describe their properties so that: - we can postulate how the graphs evolved. - understand trends in how they are put together, and perhaps how they perform their functions. - to create null models to distinguish between functional, conserved, important features, and those that are merely there by chance.
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Random Models Erdos-Renyi (1960): Create n vertices Between every pair of vertices {u,v}, add an edge with probability p . ShowGraphArray[Partition[Table[RandomGraph[15, p], {p, 0.1, 0.9, 0.1}], 3]] Expected degree is ( n -1) p
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Preferential Attachment At time step t: • Node u t is added. • Edge { v , u t } added independently with probability: k v ° w k w Proposed in the context of the WWW: popular pages become more popular.
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This note was uploaded on 01/13/2012 for the course CMSC 423 taught by Professor Staff during the Fall '07 term at Maryland.

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attack - Random Graphs 858L Descriptive Studies of...

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