# Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid

@article{Hartmann2020SearchingFS, title={Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid}, author={B{\'a}lint Hartmann and Vikt'oria Sug'ar}, journal={Scientific Reports}, year={2020}, volume={11} }

Since the introduction of small-world and scale-free properties, there is an ongoing discussion on how certain real-world networks fit into these network science categories. While the electrical power grid was among the most discussed examples of these real-word networks, published results are controversial, and studies usually fail to take the aspects of network evolution into consideration. Consequently, while there is a broad agreement that power grids are small-world networks and might show…

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## References

SHOWING 1-10 OF 40 REFERENCES

### Scale-free networks are rare

- Computer ScienceNature Communications
- 2019

A severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks finds robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws.

### How rare are power-law networks really?

- Computer ScienceProceedings of the Royal Society A
- 2020

This paper modifications the well-known Kolmogorov–Smirnov test to achieve even sensitivity along the tail, considering the dependence between the empirical degrees under the null distribution, while guaranteeing sufficient power of the test.

### The Ubiquity of Small-World Networks

- Computer ScienceBrain Connect.
- 2011

A new small-world metric, ω (omega), is proposed, which compares network clustering to an equivalent lattice network and path length to a random network, as Watts and Strogatz originally described.

### Analysis of Cascading Failures in Small-world Power Grid

- Physics, Engineering
- 2011

The development of complex network theory, especially the discovery of small-world characteristics in power grids, has made people more and more concerned on the structural vulnerability of electric…

### Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence

- Computer SciencePloS one
- 2008

A precise measure of ‘small-world-ness’ S is defined based on the trade off between high local clustering and short path length and several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing.

### Classes of small-world networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2000

Evidence of the occurrence of three classes of small-world networks, characterized by a vertex connectivity distribution that decays as a power law law, and the nature of such constraints may be the controlling factor for the emergence of different classes of networks are presented.

### Small worlds: the dynamics of networks between order and randomness

- Computer ScienceSGMD
- 2002

Everyone knows the small-world phenomenon: soon after meeting a stranger, we are surprised to discover that we have a mutual friend, or we are connected through a short chain of acquaintances. In his…

### Low-rank network decomposition reveals structural characteristics of small-world networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This work develops a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively.

### The evolution of the topology of high-voltage electricity networks

- EconomicsInt. J. Crit. Infrastructures
- 2009

This paper analyzes the growth of the French 400 kV electricity transmission network from its establishment in 1960 until the year 2000 and evaluates how the topological efficiency and vulnerability measures evolve in the course of time.

### Analysis of transmission-power-grid topology and scalability, the European case study

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2018