2009/06/22 by Onuttom Narayan, Iraj Saniee
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Computer science #Energy Efficient Wireless Sensor Networks #Mathematics #Network Traffic and Congestion Control #Scaling #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.82.036102
4 pages, 5 figures
arxiv created 2009/06/22 · openalex publication_date 2010/09/02 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k)\ensuremath∼k^\ensuremath-\ensuremathγ, we show that the load is l(k)\ensuremath∼k^\ensuremathη with \ensuremathη=\ensuremathγ\ensuremath-1, implying that the probability distribution for the load is p(l)\ensuremath∼1/l2 independent of \ensuremathγ. The results are obtained through scaling arguments supported by finite size scaling studies. They contradict earlier claims, but are in agreement with the exact solution for the special case of tree graphs. Results are also presented for real communications networks at the IP layer, using the latest available data. Our analysis of the data shows relatively poor power-law degree distributions as compared to the scaling of the load versus degree. This emphasizes the importance of the load in network analysis.