Branching Process Approach to Avalanche Dynamics on Complex Networks

D. S. Lee, K. I. Goh, B. Kahng, D. Kim

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks with general degree distributions. With the threshold height of each node given as its degree in the model, self-organized criticality emerges such that the avalanche size and the duration distribution follow power laws with exponents τ and δ, respectively, Applying the theory of the multiplicative branching process, we find that the exponents τ and δ are given as τ = γ (γ-1) and δ = (γ-1)/(γ-2) for the degree distribution pd(k) ∼ k with 2 < γ < 3, with a logarithmic correction at γ = 3, while they are 3/2 and 2, respectively, for γ > 3 and when pd(k) follows an exponential-type distribution. The analytic solutions are supported by our numerical simulation results.

Original languageEnglish
Pages (from-to)633-637
Number of pages5
JournalJournal of the Korean Physical Society
Issue number3 I
Publication statusPublished - 2004 Mar
Externally publishedYes


  • Avalanche
  • Complex network

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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