## Network Analysis

August 29, 2011 § Leave a comment

Network Analysis is very useful in that it allows us to focus on important aspects of large and complex techniques through various analysis techniques.

**Scale-Free Networks** are quite popular and useful. SFNs’ have a power-law degree distribution, at least asymptotically. This occurs in social networks (with phenomenons such as “Six Degrees of Separation (S. Milgram, John Guare (1967)), communication networks, biological networks (metabolic), world wide web (1999, 19* separation), scientific collaboration, citation patterns, etc. Power-Law Degree distribution is attributed to high clustering coefficients (i.e. “My friends will ikely know each other.”).

Exponential, or more purely random networks (road networks) have a **Poisson distribution** (following models such as Erdos-Renyi’s 1960 democratically random model). Watts-Strogatz Model; Small World Networks, simulates regular to small-world to random networks, finding that this 6 degrees of separation comes from randoms that know a bunch of people you don’t.

Essentially, Scale-Free Networks’ Network model have **exponential growth**, and **preferential attachment**. They have **power-law degree distribution**, **high clustering coefficient** and extremely **small average path length O(log log n)**. These attributes make SFN’s useful for modelling real-world networks.** **Other networks include small-world networks and power-law random sparse networks (Fan Chung).

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