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7 Pages

### c07_rand_graphs_handout

Course: PHYS 597, Fall 2009
School: Penn State
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Word Count: 1611

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models Network random graphs Properties common to many large-scale networks, independently of their origin and function: 1. The degree and betweenness distribution are decreasing functions, usually power-laws. 2. The distances scale logarithmically with the network size Random networks The average distance and clustering coefficient only depend on the number of nodes and edges in the network. This suggests that...

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models Network random graphs Properties common to many large-scale networks, independently of their origin and function: 1. The degree and betweenness distribution are decreasing functions, usually power-laws. 2. The distances scale logarithmically with the network size Random networks The average distance and clustering coefficient only depend on the number of nodes and edges in the network. This suggests that general models based only on the number of nodes and edges in the network could be successful in describing the properties of an "expected" (characteristic) network. Uniformly random network: distributes the edges uniformly among nodes. Probabilistic interpretation: There exists a set (ensemble) of networks with given number of nodes and edges. Select a random member of this set. What are the expected properties of this network? studied by random graph theory. l log N log k 3. The clustering coefficient does not seem to depend on the network size C k As though...
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