A model for dynamic communicators

Mantzaris, Alexander V.; Higham, Desmond J.

doi:10.1017/s0956792512000186

Cited by 17 publications

(15 citation statements)

References 29 publications

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“…Similarly, Huffaker [23, p. 594] identifies online leaders who 'trigger feedback, spark conversations within the community, or even shape the way that other members of a group "talk" about a topic'. Related experiments in Mantzaris & Higham [24] on e-mail and voice mail data led to the term dynamic communicators to describe individuals with an enhanced ability to disseminate or collect information relative to their centrality based on static or aggregate summaries. Our aim here is to present a framework that allows us to quantify these effects elegantly and efficiently in a continuous-time setting.…”

Section: Background On Network Centralitymentioning

confidence: 99%

A dynamical systems view of network centrality

Grindrod

Higham

2014

Proc. R. Soc. A.

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To gain insights about dynamic networks, the dominant paradigm is to study discrete snapshots, or timeslices, as the interactions evolve. Here, we develop and test a new mathematical framework where network evolution is handled over continuous time, giving an elegant dynamical systems representation for the important concept of node centrality. The resulting system allows us to track the relative influence of each individual. This new setting is natural in many digital applications, offering both conceptual and computational advantages. The novel differential equations approach is convenient for modelling and analysis of network evolution and gives rise to an interesting application of the matrix logarithm function. From a computational perspective, it avoids the awkward up-front compromises between accuracy, efficiency and redundancy required in the prevalent discrete-time setting. Instead, we can rely on state-of-the-art ODE software, where discretization takes place adaptively in response to the prevailing system dynamics. The new centrality system generalizes the widely used Katz measure, and allows us to identify and track, at any resolution, the most influential nodes in terms of broadcasting and receiving information through time-dependent links. In addition to the classical static network notion of attenuation across edges, the new ODE also allows for attenuation over time, as information becomes stale. This allows 'running measures' to be computed, so that networks can be monitored in real time over arbitrarily long intervals. With regard to computational efficiency, we explain why it is cheaper to track good receivers of information than good broadcasters. An important consequence is that the overall broadcast activity in the network can also be monitored efficiently. We use two synthetic examples to validate the relevance of the new measures. We then illustrate the ideas on a large-scale voice call network, where key features are discovered that are not evident from snapshots or aggregates.

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Section: Background On Network Centralitymentioning

confidence: 99%

A dynamical systems view of network centrality

Grindrod

Higham

2014

Proc. R. Soc. A.

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“…In other words, broadcast and receive centralities are related by a reversal of the time ordering. Synthetic examples in [12] and [23] illustrate that broadcast centrality (BC) and receive centrality (RC) measures perform better than aggregated measures in identifying nodes with time-sensitive links as important. The term dynamic communicator coined in [23] refers precisely to the nodes which rank highly in the dynamic sense but do not stand out in a snapshot or aggregate view of the network.…”

Section: Dynamic Communicabilitymentioning

confidence: 99%

“…We are motivated by examples in [23] and [40] which show that centrality measures based on time-aggregated versions of temporal networks (as shown in Fig. 2) fail to adequately capture important nodes.…”

Section: Introductionmentioning

confidence: 99%

Dynamic communicability and epidemic spread: a case study on an empirical dynamic contact network

et al. 2016

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We analyze a recently proposed temporal centrality measure applied to an empirical network based on person-to-person contacts in an emergency department of a busy urban hospital. We show that temporal centrality identifies a distinct set of top-spreaders than centrality based on the time-aggregated binarized contact matrix, so that taken together, the accuracy of capturing top-spreaders improves significantly. However, with respect to predicting epidemic outcome, the temporal measure does not necessarily outperform less complex measures. Our results also show that other temporal markers such as duration observed and the time of first appearance in the the network can be used in a simple predictive model to generate predictions that capture the trend of the observed data remarkably well.

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“…The alternative walk-counting approach in [5] was based on a direct generalization of Katz centrality [6] to the case of time-dependent networks. A key message from [13] and [8] is that centrality measures based on a static, aggregate summary of the network will not adequately reflect the hierarchy of importance.…”

Section: Background and Motivationmentioning

confidence: 99%

Dynamic Communicability Predicts Infectiousness

Mantzaris

Higham

2013

Understanding Complex Systems

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Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality measures, which are relatively inexpensive to compute, assign rankings to individual nodes based on their ability to broadcast information over the dynamic topology. We compare these with node rankings based on infectiousness that arise when a full stochastic SI simulation is performed over the dynamic network. More precisely, we look at the proportion of the network that a node is able to infect over a fixed time period, and the length of time that it takes for a node to infect half the network. We find that the dynamic centrality measures are an excellent, and inexpensive, proxy for the full simulation-based measures.

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A model for dynamic communicators

Cited by 17 publications

References 29 publications

A dynamical systems view of network centrality

A dynamical systems view of network centrality

Dynamic communicability and epidemic spread: a case study on an empirical dynamic contact network

Dynamic Communicability Predicts Infectiousness

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