Controllability of deterministic networks with the identical degree sequence
Xiujuan Ma1, Haixing Zhao2, Binghong Wang3
1School of Computer Science, Shaanxi Normal University, Xi'an, Shaanxi, 710062, P. R. China; School of Computer Science, Qinghai Normal University, Xining, Qinghai, 810008, P. R. China.
Plos One
|May 29, 2015
Summary
Controlling complex networks is crucial. This study shows that while degree distribution is important, it alone doesn't fully determine the controllability of deterministic, unweighted, undirected networks.
Area of Science:
- Network Science
- Network Engineering
- Graph Theory
Background:
- Controllability of complex networks is vital in science and engineering.
- Network topology significantly influences controllability.
- Degree distribution was hypothesized to be a key factor in network controllability.
Purpose of the Study:
- To analyze the effect of degree distribution on network controllability.
- To investigate deterministic networks with identical degree sequences, specifically (x,y)-flower networks.
- To determine if degree distribution alone is sufficient to characterize controllability.
Main Methods:
- Introduced a class of deterministic networks called (x,y)-flower networks.
- Applied exact controllability theory to analyze (1, 3)-flower and (2, 2)-flower networks.
- Conducted simulations to compare the controllability of different (x,y)-flower networks.
Main Results:
- Identified the minimum number of driver nodes required for controllability in specific (x,y)-flower networks.
- Demonstrated that (x,y)-flower networks with identical degree sequences exhibit distinct controllability.
- Found that degree distribution is insufficient to fully characterize controllability in deterministic, unweighted, undirected networks.
Conclusions:
- Degree distribution alone does not sufficiently determine the controllability of deterministic, unweighted, and undirected networks.
- Network structure beyond degree sequence plays a critical role in controllability.
- Further research is needed to identify comprehensive metrics for network controllability.
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