Special Attention Network

Abstract

In this Note a social network model for opinion formation is proposed in which a person connected to $q$ partners pays an {\em attention} $1/q$ to each partner. The mutual attention between two connected persons $i$ and $j$ is taken equal to the geometric mean $1/\sqrt{q_i{q}_j}$. Opinion is represented as usual by an Ising spin $s=\pm 1$ and mutual attention is given through a two-spin coupling $J_{ij}=JQ/\sqrt{q_i{q}_j}$, $Q$ being the average connectivity in the network. Connectivity diminishes attention and only persons with low connectivity can pay special attention to each other leading to a durable common (or opposing) opinion. The model is solved in "mean-field" approximation and a critical "temperature" $T_c$ proportional to $JQ$ is found, which is independent of the number of persons $N$, for large $N$.

5 pages, no figures

References in corpus (6)

• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Mean field solution of the Ising model on a Barabasi-Albert network
• Critical phenomena in networks
• First- and second-order phase transitions in scale-free networks

Cited by in corpus (20)

• Statistical physics of social dynamics
• Ising model simulation in directed lattices and networks
• Trading interactions for topology in scale-free networks
• Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
• Ising model on the Apollonian network with node dependent interactions
• Majority-vote on directed Small-World networks
• Criticality on networks with topology-dependent interactions
• Noise in random Boolean networks
• Impact of site dilution and agent diffusion on the critical behavior of the majority-vote model
• Redundancy and error resilience in Boolean Networks
• Percolation on bipartite scale-free networks
• Opinion Diversity and Social Bubbles in Adaptive Sznajd Networks
• Boolean networks with robust and reliable trajectories
• Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks
• An energy-based interaction model for population opinion dynamics with topic coupling
• Ising model with spins S=1/2 and 1 on directed and undirected Erdös-Rényi random graphs
• Properties of weighted complex networks
• The behavior of noise-resilient Boolean networks with diverse topologies
• Ising model for distribution networks
• A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution