No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Robust detection of dynamic community structure in networks
1. M. E. J. Newman, Networks: An Introduction (Oxford University Press, 2010).
8. T. J. Fararo and J. Skvoretz, in Status, Network, and Structure: Theory Development in Group Processes (Stanford University Press, 1997), pp. 362–386.
11. A. S. Waugh
, L. Pei
, J. H. Fowler
, P. J. Mucha
, and M. A. Porter
, “ Party polarization in Congress: A network science approach
16. M. A. Porter, J.-P. Onnela, and P. J. Mucha, Not. Am. Math. Soc. 56, 1082 (2009).
17. H. Simon, Proc. Am. Philos. Soc. 106, 467 (1962).
27. S. Hutchings, “ The behavior of modularity-optimizing community detection algorithms,” M.Sc. Thesis (University of Oxford, 2011).
36.Equation (4) gives the definition for the notion of stationarity that we used in Ref. 4. The equation for this quantity in Ref. 4 has a typo in the denominator. We wrote incorrectly in that paper that the denominator was , whereas the numerical computations in that paper used .
37.In other areas of investigation, it probably should be.
41. J. Wang, L. Wang, Y. Zang, H. Yang, H. Tang, Q. Gong, Z. Chen, C. Zhu, and Y. He, Hum. Brain Mapp 30, 1511 (2009).
48. M. Kim and J. Leskovec, SIAM International Conference on Data Mining (2011).
49. O. Sporns, Networks of the Brain (MIT, 2010).
52. Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002).
57. V. D. Blondel, J. L. Guillaume, R. Lambiotte, and E. Lefebvre, J. Stat. Mech. 10, P10008 (2008).
59.A discrete time series can be represented as a vector. A continuous time series would first need to be discretized.
61.The code used for this computation actually operates on . However, this should be an equivalent mathematical estimate to the same computation on , which is the same except for a set of measure zero.
65.It is also important to note that the AAFT method can allow nonlinear correlations to remain in the surrogate data. Therefore, the development of alternative surrogate data generation methods might be necessary (Refs. 83 and 84).
66.In the descriptions below, we use terms like “random” rewiring to refer to a process that we are applying uniformly at random aside from specified constraints.
Article metrics loading...
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (“optimization variance”) and over randomizations of network structure (“randomization variance”). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.
Full text loading...
Most read this month