Generalized theory for node disruption in finite-size complex networks

Bivas Mitra (1) , Niloy Ganguly (1) , Sujoy Ghose (1) , Fernando Peruani (2, 3)

1 IIT Kharagpur - Indian Institute of Technology Kharagpur
2 ISC-PIF - Institut des Systèmes Complexes - Paris Ile-de-France
3 SPEC - UMR3680 - Service de physique de l'état condensé

After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula. Based on this expression, we derive a general condition for the stability of noncorrelated finite complex networks under any arbitrary attack. We apply this formalism to derive an expression for the percolation threshold fc under a general attack of the form fk∼kγ, where fk stands for the probability of a node of degree k of being removed during the attack. We show that fc of a finite network of size N exhibits an additive correction which scales as N−1 with respect to the classical result for infinite networks.

Domaines: Biophysique [physics.bio-ph]; Modélisation et simulation; Réseaux et télécommunications [cs.NI]

Bivas Mitra, Niloy Ganguly, Sujoy Ghose, Fernando Peruani. Generalized theory for node disruption in finite-size complex networks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78 (2), pp.026115. ⟨10.1103/PhysRevE.78.026115⟩. ⟨hal-00905224⟩