2003/04/30 by S. S. Manna
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Psychology · #Complex Network Analysis Techniques #Mental Health Research Topics #Opinion Dynamics and Social Influence #cond-mat.stat-mech #q-bio
paper · pdf · doi:10.1103/physreve.68.027104
published as Phys. Rev. E. 68, 027104 (2003) · 4 pages, 4 figures
openalex publication_date 2003/08/20 · arxiv created 2003/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A dynamic model of a society is studied where each person is an uncorrelated and noninteracting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. This network exhibits a different percolationlike phase transition in all dimensions. On introducing simultaneous death and birth rates in the population, we show that the friendship network shows the six degrees of separation for ever after where the precise value of the network diameter depends on the death/birth rate. A susceptible-infected-susceptible-type model of disease spreading shows that this society always remains healthy if the population density is less than certain threshold value.