Mechanism for linear preferential attachment in growing networks

2005/05/11 by X. P. Xu, Xinping Xu, Feng Liu +2 · 2 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Opinion Dynamics and Social Influence #physics.data-an #physics.soc-ph

paper · pdf · doi:10.1016/j.physa.2005.04.005

published as Physica A 356(2005)662 · 10 pages, 1 figure

openalex publication_date 2005/05/11 · arxiv created 2007/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse growing networks. This provides theoretical evidence in support of the linear preferential attachment widely exists in real networks and adopted as a crucial assumption in growing network models. Besides, in the sparse limit, we develop a method to calculate the degree correlation and clustering coefficient in our ensemble model, which is suitable for all kinds of sparse networks including the BA model, proposed by Barabasi and Albert.

Citations

• Emergence of scaling in random networks
• Preferential Attachment in the Protein Network Evolution
• Scale-free networks from a Hamiltonian dynamics
• Statistical mechanics of complex networks
• The large-scale organization of metabolic networks

Cited by

• Growing Small-World Networks Based on a Modified BA Model
• A novel configuration model for random graphs with given degree sequence