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A stochastic complex network model
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## A stochastic complex network model

### David J. Aldous

**Abstract.**
We introduce a stochastic model for complex networks possessing three qualitative features: power-law degree distributions, local clustering, and slowly growing diameter. The model is mathematically natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters.

*Copyright 2003 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**09** (2003), pp. 152-161
- Publisher Identifier: S 1079-6762(03)00123-9
- 2000
*Mathematics Subject Classification*. Primary 60K35; Secondary 05C80, 90B15, 94C15
*Key words and phrases*. Complex network, Poisson process, PWIT, random graph, scale-free, small worlds, Yule process
- Received by editors July 22, 2003
- Posted on December 18, 2003
- Communicated by Ronald L. Graham
- Comments (When Available)

**David J. Aldous**

Department of Statistics, 367 Evans Hall, U.C. Berkeley, CA 94720

*E-mail address:* `aldous@stat.berkeley.edu`

The author was supported in part by NSF Grant DMS-0203062.

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