# The degree sequence of a scale-free random graph process

## Abstract

Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many steps the proportion P(d) of vertices with degree d should obey a power law P(d) α d-γ. They obtained γ - 2.9 ± 0.1 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain P(d) asymptotically for all d ≤ n1/15, where n is the number of vertices, proving as a consequence that γ = 3.

## Publication Title

The Structure and Dynamics of Networks

## Recommended Citation

Bollobás, B., Riordan, O., Spencer, J., & Tusnády, G.
(2011). The degree sequence of a scale-free random graph process.* The Structure and Dynamics of Networks**, 9781400841356*, 385-395.
Retrieved from https://digitalcommons.memphis.edu/facpubs/5852