Small-world behavior in time-varying graphs

Tang, John; Scellato, Salvatore; Musolesi, Mirco; Mascolo, Cecilia; Latora, Vito

doi:10.1103/physreve.81.055101

Cited by 275 publications

(228 citation statements)

References 29 publications

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“…Such a study would be even richer in the temporal network framework where the motifs would represent temporal subnetworks. There are, to our knowledge, only a few papers where the time domain is directly taken into account: Valencia et al [156] study functional brain networks reconstructed from MEG data with the phase-locking criterion, and show that the functional connectivity varies with time and frequency during the processing of visual stimuli, while certain network features such as small-world characteristics are maintained (see also [149] [12] monitor the evolution of a brain network while the subject is learning a simple motor task. In addition, it would be of great interest to measure the dynamics of functional networks when the applied stimulus is also time-dependent, especially with naturalistic (close-toreal-life) paradigms such as watching a movie or listening to music in the fMRI scanner (see e.g.…”

Section: G Neural and Brain Networkmentioning

confidence: 99%

“…the closeness centrality measures the inverse total distance to all other vertices and is high for vertices who are close to all others. Similarly, for temporal networks, one may be interested in how quickly a vertex may on average reach other vertices, and define the temporal closeness centrality as [149] …”

Section: Centrality Measuresmentioning

confidence: 99%

“…8. One of the curves in this figure corresponds to a nifty measure of the similarity in the connection pattern of a vertex i by the adjacency correlation function (also called temporal-correlation coefficient in [149])…”

Section: J Persistent Patternsmentioning

confidence: 99%

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Temporal networks

2012

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A great variety of systems in nature, society and technology-from the web of sexual contacts to the Internet, from the nervous system to power grids-can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks. The study of temporal networks is very interdisciplinary in nature. Reflecting this, even the object of study has many names

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Section: G Neural and Brain Networkmentioning

confidence: 99%

Section: Centrality Measuresmentioning

confidence: 99%

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Temporal networks

2012

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“…Consequently, temporal-network metrics have been introduced, since they allow a better understanding of the dynamic properties of such systems. In addition, it has been shown [2,3] that such temporal aspects cannot be ignored, otherwise the system performance can be greatly overestimated.…”

Section: Introductionmentioning

confidence: 99%

Error and attack vulnerability of temporal networks

2012

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The study of real-world communication systems via complex network models has greatly expanded our understanding on how information flows, even in completely decentralized architectures such as mobile wireless networks. Nonetheless, static network models cannot capture the time-varying aspects and, therefore, various temporal metrics have been introduced. In this paper, we investigate the robustness of time-varying networks under various failures and intelligent attacks. We adopt a methodology to evaluate the impact of such events on the network connectivity by employing temporal metrics in order to select and remove nodes based on how critical they are considered for the network. We also define the temporal robustness range, a new metric that quantifies the disruption caused by an attack strategy to a given temporal network. Our results show that in real-world networks, where some nodes are more dominant than others, temporal connectivity is significantly more affected by intelligent attacks than by random failures. Moreover, different intelligent attack strategies have a similar effect on the robustness: even small subsets of highly connected nodes act as a bottleneck in the temporal information flow, becoming critical weak points of the entire system. Additionally, the same nodes are the most important across a range of different importance metrics, expressing the correlation between highly connected nodes and those that trigger most of the changes in the optimal information spreading. Contrarily, we show that in randomly generated networks, where all the nodes have similar properties, random errors and intelligent attacks exhibit similar behavior. These conclusions may help us in design of more robust systems and fault-tolerant network architectures.

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“…Although the fundamental ideas in this area were developed to analyse a single, static network, there is a growing need to develop tools for the dynamic case, where links appear and disappear in a time-dependent manner. Key application areas include voice calls [9,14], email activity [3,14], online social interaction [29], geographical proximity of mobile device users [17], voting and trading patterns [1,25] and neural activity [4,12].…”

Section: Motivationmentioning

confidence: 99%

Dynamic Targeting in an Online Social Medium

Laflin

Mantzaris

Ainley

et al. 2012

Lecture Notes in Computer Science

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Abstract. Online human interactions take place within a dynamic hierarchy, where social influence is determined by qualities such as status, eloquence, trustworthiness, authority and persuasiveness. In this work, we consider topic-based Twitter interaction networks, and address the task of identifying influential players. Our motivation is the strong desire of many commerical entities to increase their social media presence by engaging positively with pivotal bloggers and tweeters. After discussing some of the issues involved in extracting useful interaction data from a Twitter feed, we define the concept of an active node subnetwork sequence. This provides a time-dependent, topic-based, summary of relevant Twitter activity. For these types of transient interactions, it has been argued that the flow of information, and hence the influence of a node, is highly dependent on the timing of the links. Some nodes with relatively small bandwidth may turn out to be key players because of their prescience and their ability to instigate follow-on network activity. To simulate a commercial application, we build an active node subnetwork sequence based on key words in the area of travel and holidays. We then compare a range of network centrality measures, including a recently proposed version that accounts for the arrow of time, with respect to their ability to rank important nodes in this dynamic setting. The centrality rankings use only connectivity information (who Tweeted whom, when), but if we post-process the results by examining account details, we find that the time-respecting, dynamic, approach, which looks at the follow-on flow of information, is less likely to be 'misled' by accounts that appear to generate large numbers of automatic Tweets with the aim of pushing out web links. We then benchmark these algorithmically derived rankings against independent feedback from five social media experts who judge Twitter accounts as part of their professional duties. We find that the dynamic centrality measures add value to the expert view, and indeed can be hard to distinguish from an expert in terms of who they place in the top ten. We also highlight areas where the algorithmic approach can be refined and improved.

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Small-world behavior in time-varying graphs

Cited by 275 publications

References 29 publications

Temporal networks

Temporal networks

Error and attack vulnerability of temporal networks

Dynamic Targeting in an Online Social Medium

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