Temporal networks

Holme, Petter; Saramäki, Jari

doi:10.1016/j.physrep.2012.03.001

Cited by 2,323 publications

(2,004 citation statements)

References 157 publications

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“…Although the correlation decreases along the generations in the present analysis as shown in Eq. (25), in reality, the covariance matrix is not necessarily of the form which we considered here.…”

Section: Discussionmentioning

confidence: 99%

Viral spreading of daily information in online social networks

Kawamoto

Hatano

2014

Physica A: Statistical Mechanics and its Applications

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We explain a possible mechanism of an information spreading on a network which spreads extremely far from a seed node, namely the viral spreading. On the basis of a model of the information spreading in an online social network, in which the dynamics is expressed as a random multiplicative process of the spreading rates, we will show that the correlation between the spreading rates enhances the chance of the viral spreading, shifting the tipping point at which the spreading goes viral.

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Section: Discussionmentioning

confidence: 99%

Viral spreading of daily information in online social networks

Kawamoto

Hatano

2014

Physica A: Statistical Mechanics and its Applications

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“…The Wikipedia data discussed earlier could be used to probe such effects, since it captures snapshots of Wikipedia at different times during the network's evolution. It would be interesting to quantify differences in the effects (if any) of BFS and random sampling on time-varying or temporal networks [58]. A natural question, after analyzing the drawbacks of sampling procedures, will be how we can overcome such problems to get unbiased network samplings.…”

Section: Summary and Discussionmentioning

confidence: 99%

Sampling properties of directed networks

Son

Christensen²,

Bizhani³

et al. 2012

Phys. Rev. E

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For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.

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“…2 The formalism of temporal networks is convenient for studying data drawn from areas such as person-to-person communication (e.g., via mobile phones 5,6 ), one-to-many information dissemination (such as Twitter networks 7 ), cell biology, distributed computing, infrastructure networks, neural and brain networks, and ecological networks. 2 Important phenomena that can be studied in this framework include network constraints on gang and criminal activity, 8,9 political processes, 10,11 human brain function, 4,12 human behavior, 13 and financial structures. 14,15 Time-dependent complex systems can have densely connected components in the form of cohesive groups of nodes known as "communities" (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Robust detection of dynamic community structure in networks

Bassett

Porter

Wymbs

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

450

617

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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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Temporal networks

Cited by 2,323 publications

References 157 publications

Viral spreading of daily information in online social networks

Viral spreading of daily information in online social networks

Sampling properties of directed networks

Robust detection of dynamic community structure in networks

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