2003/01/31 by Ginestra Bianconi
Mathematics · Physics and Astronomy · Psychology · #Combinatorics #Complex Network Analysis Techniques #Computer network #Computer science #Constant (computer programming) #Discrete mathematics #Logarithm #Mathematical analysis #Mathematics #Mental Health Research Topics #Metric (unit) #Network topology #Node (physics) #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Time complexity #Topology (electrical circuits) #Tree (set theory) #Tree network #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.67.056119
5 pages,8 figures
arxiv created 2003/03/13 · openalex publication_date 2003/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed, focusing on the directed distance of nodes from the origin. The topology of the networks strongly depends on the dynamical parameter T, called the temperature. At T= infinity we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes), while the fermionic network grows following a single branch of the tree, and the distance from the origin varies as a power law of the number of nodes in the network.