2009/01/01 by Parongama Sen · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · Mathematics · Physics and Astronomy · #Chemistry #Combinatorics #Complex Network Analysis Techniques #Complex network #Context (archaeology) #Degree (music) #Degree distribution #Diffusion and Search Dynamics #Distribution (mathematics) #Engineering #Exponential distribution #Exponential function #Fraction (chemistry) #Geography #Mathematical analysis #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Physics #Power law #Quantum mechanics #Range (aeronautics) #Statistical physics #Statistics #Value (mathematics) #physics.soc-ph
paper · pdf · doi:10.1007/978-3-642-02469-6_49
published in Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 1719-1730 · Talk given in Complex2009, Shanghai; some results reported earlier in arXiv:0801.0370
openalex publication_date 2009/01/01 · arxiv created 2009/03/24 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity f of a node as the fraction of successful dynamic paths through it with a fixed target. The distribution D(f) of the fraction of nodes with funnelling capacity f shows a power law behaviour in random networks (with power law or stretched exponential degree distribution) for a considerable range of values of the parameters defining the networks. Specifically we study in detail D1=D(f=1), which is the quantity signifying the presence of nodes through which all the dynamical paths pass through. In scale free networks with degree distribution P(k) ∝ k-γ, D1 increases linearly with γ initially and then attains a constant value. It shows a power law behaviour, D1 ∝ N-ρ, with the number of nodes N where ρ is weakly dependent on γ for γ> 2.2. The latter variation is also independent of the number of searches. On stretched exponential networks with P(k) ∝ exp(-kδ), ρ is strongly dependent on δ. The funnelling distribution for a model social network, where the question of funnelling is most relevant, is also investigated.