2. Real vs. Random
• Many real networks grow.
• These have highly skewed degree
distributions: often a power law.
• Random graphs usually have Poisson
distribution
3. The Model
• Start from a single vertex without edges.
• At each step a vertex is added.
• With probability δ, two vertices are joined with
an undirected edge.
• At time t: t vertices and δt (avg.) edges.
• Different from preferential attachment model.
12. References
Are randomly grown graphs really random?
Callaway et al, arXiv:cond-mat/0104546v2, 14 June 2001
M. Molloy and B. Reed, Random Structures and
Algorithms 6, 161 (1995).
M. Molloy and B. Reed, Combinatorics,
Probability and Computing 7, 295 (1998).