E Ben-Naim and P L Krapivsky 2007 J. Phys. A: Math. Theor. 40 8607 doi:10.1088/1751-8113/40/30/001
E Ben-Naim1 and P L Krapivsky2
Show affiliationsWe 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−β as k → ∞. The exponent β = 2 + (r − 1)−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.
89.75.Hc Networks and genealogical trees
02.50.Ng Distribution theory and Monte Carlo studies
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
60Exx Distribution theory (See also 62Exx, 62Hxx)
Issue 30 (27 July 2007)
Received 25 April 2007, in final form 1 June 2007
Published 12 July 2007
E Ben-Naim and P L Krapivsky 2007 J. Phys. A: Math. Theor. 40 8607
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