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Localization in random bipartite graphs: Numerical and empirical study
1Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic.
Physical Review. E
|June 17, 2017
Summary
We studied bipartite graphs with power-law distributions, finding the mobility edge depends on degree distribution and graph size. Localization vanishes at the jamming threshold, impacting granular matter and social networks.
Area of Science:
- Complex networks
- Statistical physics
- Network science
Background:
- Bipartite graphs with power-law degree distributions model various systems, including granular matter and social networks.
- Understanding the mobility edge is crucial for characterizing wave localization and transport properties in these networks.
Purpose of the Study:
- To investigate the behavior of the mobility edge in bipartite graphs with power-law degree distributions.
- To determine the influence of degree distribution power and the ratio of partition sizes on the mobility edge.
- To analyze the multifractal spectrum in different phases and examine the Amazon reviewer-item network.
Main Methods:
- Analysis of adjacency matrices of bipartite graphs.
- Theoretical determination of the mobility edge position.
- Investigation of the multifractal spectrum.
- Empirical study of the Amazon reviewer-item network.
Main Results:
- The mobility edge's position is strongly dependent on the degree distribution's power and the graph's partition size ratio.
- Localization vanishes at the jamming threshold (equal partition sizes).
- A nontrivial multifractal spectrum is observed in the delocalized phase near the mobility edge.
- The mobility edge disappears in the empirical Amazon reviewer-item network.
Conclusions:
- The mobility edge's behavior is sensitive to network structure and degree distribution properties.
- The disappearance of the mobility edge in the Amazon network suggests unique properties compared to theoretical models.
- Findings have implications for understanding vibrational states in granular systems and information flow in social networks.
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