Non-parametric resampling of random walks for spectral network clustering

@article{Fallani2014NonparametricRO,
  title={Non-parametric resampling of random walks for spectral network clustering},
  author={Fabrizio de Vico Fallani and Vincenzo Nicosia and Vito Latora and Mario Chavez},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2014},
  volume={89 1},
  pages={
          012802
        }
}
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show… 

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References

SHOWING 1-10 OF 67 REFERENCES
Dynamical Processes on Complex Networks
TLDR
A new and recent account presents a comprehensive explanation of the effect of complex connectivity patterns on dynamical phenomena in a vast number of everyday systems that can be represented as large complex networks.
Networks: An Introduction
TLDR
This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Social Network Analysis
This paper reports on the development of social network analysis, tracing its origins in classical sociology and its more recent formulation in social scientific and mathematical work. It is argued
Spectral Graph Theory
Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigenvalues and quasi-randomness Expanders and explicit constructions Eigenvalues
Spectra of Graphs: Theory and Applications
Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The
APPL
TLDR
A prototype probability package named APPL (A Probability Programming Language) is presented that can be used to manipulate random variables and examples illustrate its use.
Res
In Palfreyman & Tapper (2014) ‘Reshaping the University: The Rise of the Regulated Market in Higher Education’ (Oxford University Press) we have tried to explain how English HE has reached the
Chaos
or "What a lie", or "How could I have said so"? or demanded at once that she should be sent for. Yet, he never on one single occasion, before others, spoke to Mrs. Cox on the subject. The only
Nature
  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
...
...