Constrained randomization of weighted networks

Ansmann, Gerrit; Lehnertz, Klaus

doi:10.1103/physreve.84.026103

Cited by 30 publications

(60 citation statements)

References 60 publications

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“…In order to compare different types of networks, a thorough, concise, and general definition of link weights must be found as otherwise no useful intercomparison of obtained weighted network characteristics is possible. In order to develop a corresponding framework, our models could be combined with existing models for non-spatially embedded weighted networks [57] that follow a similar strategy of constrained rewiring of a given network as the models presented in this work.…”

Section: Discussionmentioning

confidence: 99%

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

et al. 2016

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Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

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Section: Discussionmentioning

confidence: 99%

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

et al. 2016

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“…67 To retain both the mean and distribution of edge weights, one can employ a permutation-based connectional null model that randomly rewires network edges with no additional constraints by reassigning uniformly at random the entire set of matrix elements A ijl in the lth layer (i.e., the matrix A l ). Other viable connectional null models include ones that preserve degree 21,68 or strength 69 distributions, or-for networks based on time-series datapreserve length, frequency content, and amplitude distribution of the original time series. 70 In this section, we present results for a few null models that are applicable to a variety of temporal networks.…”

Section: Intra-layer and Inter-layer Null Modelsmentioning

confidence: 99%

Robust detection of dynamic community structure in networks

Bassett

Porter

Wymbs

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

484

645

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We describe techniques for the robust detection of community structure in some classes of timedependent 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. Many social, physical, technological, and biological systems can be modeled as networks composed of numerous interacting parts. 1 As an increasing amount of time-resolved data has become available, it has become increasingly important to develop methods to quantify and characterize dynamic properties of temporal networks. 2 Generalizing the study of static networks, which are typically represented using graphs, to temporal networks entails the consideration of nodes (representing entities) and/or edges (representing ties between entities) that vary in time. As one considers data with more complicated structures, the appropriate network analyses must become increasingly nuanced. In the present paper, we discuss methods for algorithmic detection of dense clusters of nodes (i.e., communities) by optimizing quality functions on multilayer network representations of temporal networks. 3,4 We emphasize the development and analysis of different types of null-model networks, whose appropriateness depends on the structure of the networks one is studying as well as the construction of representative partitions that take advantage of a multilayer network framework. To illustrate our ideas, we use ensembles of time-dependent networks from the human brain and human behavior.

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“…Other directions for future research could be to look at weighted networks (e.g., to integrate our ideas with those in papers such as [31]) or at bipartite networks (which also have interesting applications; see, e.g., [32]). Furthermore, it would seem appropriate in the field of network hypothesis testing to take more seriously the nontrivial number of short loops in biological signaling systems.…”

Section: Discussionmentioning

confidence: 99%

Unbiased degree-preserving randomization of directed binary networks

Roberts

Coolen

2012

Phys. Rev. E

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Randomizing networks using a naive "accept-all" edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees. The acceptance probabilities can also be generalized to define Markov chains that target any alternative desired measure on the space of directed graphs in order to generate graphs with more sophisticated topological features. This is demonstrated by defining a process tailored to the production of directed graphs with specified degree-degree correlation functions. The theory is implemented numerically and tested on synthetic and biological network examples.

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Constrained randomization of weighted networks

Cited by 30 publications

References 60 publications

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

Robust detection of dynamic community structure in networks

Unbiased degree-preserving randomization of directed binary networks

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