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Statistics of weighted treelike networks
E Almaas1, P L Krapivsky, S Redner
1Center for Network Research and Department of Physics, University of Notre Dame, Notre Dame, IN 46617, USA. ealmaas@nd.edu
Summary
This study analyzes growing tree networks with weighted links. The total network weight scales with the number of nodes (N), with specific growth patterns depending on network parameters.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Growing networks are fundamental models in various scientific domains.
- Understanding the statistical properties of these networks is crucial for predicting their behavior.
- Link weights significantly influence network dynamics and structure.
Purpose of the Study:
- To investigate the statistical properties of growing tree networks with degree-dependent link weights.
- To analyze the total network weight and link weight distribution.
- To determine the node strength scaling in these networks.
Main Methods:
- Mathematical analysis of network growth governed by preferential attachment.
- Calculation of total network weight as a function of the number of nodes (N).
- Derivation of link weight distribution and node strength scaling.
Main Results:
- The total network weight generally grows linearly with N for lambda > theta-1, and superlinearly otherwise.
- The link weight distribution exhibits a power-law form, with a logarithmic correction when lambda=0.
- Node strength scaling with node degree (k) and N is determined.
Conclusions:
- The study provides analytical predictions for the statistical properties of growing weighted networks.
- The findings offer insights into the structure and evolution of complex systems with preferential attachment.
- The results are applicable to understanding real-world networks such as social or biological networks.