2007/03/24 by E. Ben-Naim, E. Ben‐Naim, P. L. Krapivsky · 37 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree (music) #Degree distribution #Distribution (mathematics) #Exponent #Fraction (chemistry) #Gene Regulatory Network Analysis #Mathematical analysis #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Physics #Topology (electrical circuits) #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/40/30/001
published in Journal of Physics A Mathematical and Theoretical 40(30), 8607-8619 (Institute of Physics) · 8 pages, 5 figures
arxiv created 2007/03/24 · openalex publication_date 2007/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, ck ~ k-beta, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.