Elementary models of dynamic networks

Gulyás, László; Kampis, George; Legendi, Richard O.

doi:10.1140/epjst/e2013-01928-6

Cited by 10 publications

(10 citation statements)

References 10 publications

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“…Without link removal ( K = 0%), we observed that in the Erős-Rényi random network, link turnover resulted in interrupted disease spread compared to the static case, with decreasing final outbreak sizes as the turnover rate increased. These results are consistent with other studies of epidemic outcomes as a function of network dynamics (Fefferman and Ng, 2007; Gulyás et al, 2013). The relative performance of the four link removal algorithms is similar to the static case: reactive algorithms vastly outperform preventive ones and removing links in order of S-I edge centrality achieved the smallest outbreak sizes for small link removal budgets, while optimal quarantining averts a substantial number of infections once the link removal budget exceeds a threshold ( K = 20% in this case).…”

Section: Performance Of Link Removal Algorithmssupporting

confidence: 93%

“…Using the dynamic network framework described by Gulyás et al (2013) and Gulyás and Kampis (2013), we simulated outbreaks in networks with different rates of link turnover, determined by the rate of link acquisition. We set the rate of link termination such that it balanced the process of link formation to maintain the same number of links in the network, on average, over time.…”

Section: Performance Of Link Removal Algorithmsmentioning

confidence: 99%

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Link removal for the control of stochastically evolving epidemics over networks: A comparison of approaches

Enns

Brandeau

2015

Journal of Theoretical Biology

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For many communicable diseases, knowledge of the underlying contact network through which the disease spreads is essential to determining appropriate control measures. When behavior change is the primary intervention for disease prevention, it is important to understand how to best modify network connectivity using the limited resources available to control disease spread. We describe and compare four algorithms for selecting a limited number of links to remove from a network: two “preventive” approaches (edge centrality, R0 minimization), where the decision of which links to remove is made prior to any disease outbreak and depends only on the network structure; and two “reactive” approaches (S-I edge centrality, optimal quarantining), where information about the initial disease states of the nodes is incorporated into the decision of which links to remove. We evaluate the performance of these algorithms in minimizing the total number of infections that occur over the course of an acute outbreak of disease. We consider different network structures, including both static and dynamic Erdős-Rényi random networks with varying levels of connectivity, a real-world network of residential hotels connected through injection drug use, and a network exhibiting community structure. We show that reactive approaches outperform preventive approaches in averting infections. Among reactive approaches, removing links in order of S-I edge centrality is favored when the link removal budget is small, while optimal quarantining performs best when the link removal budget is sufficiently large. The budget threshold above which optimal quarantining outperforms the S-I edge centrality algorithm is a function of both network structure (higher for unstructured Erdős-Rényi random networks compared to networks with community structure or the real-world network) and disease infectiousness (lower for highly infectious diseases). We conduct a value-of-information analysis of knowing which nodes are initially infected by comparing the performance improvement achieved by reactive over preventive strategies. We find that such information is most valuable for moderate budget levels, with increasing value as disease spread becomes more likely (due to either increased connectedness of the network or increased infectiousness of the disease).

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Section: Performance Of Link Removal Algorithmssupporting

confidence: 93%

Section: Performance Of Link Removal Algorithmsmentioning

confidence: 99%

Link removal for the control of stochastically evolving epidemics over networks: A comparison of approaches

Enns

Brandeau

2015

Journal of Theoretical Biology

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“…The most classical approach consists in splitting time into slices and then building a graph, often called snapshot, for each time slice: its nodes and links represent the interactions that occurred during this time slice. One obtains a sequence of snapshots (one for each slice), and may study the time-evolution of their properties, see for instance [65,43,61,27,7,79], among many others. In [3], the authors even design a general framework to combine and aggregate wide classes of temporal properties, thus providing a unified approach for snapshot sequence studies.…”

Section: Related Workmentioning

confidence: 99%

Stream graphs and link streams for the modeling of interactions over time

Latapy

Viard

Magnien

2018

Soc. Netw. Anal. Min.

177

209

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Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.

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“…if sa < s b then 8: sc ← sa; vc ← va 21: c.append((sc, fc, vc)) 22: return standard(c) a = [(1, 5, 2), (6, 8, 1), (11,12,3), (14,16,2), (17,18,5), (19, 20, 1)] b = [(2, 3, 4), (4, 7, 3), (9, 10, 2), (13,15,5), (16, 21, 1)]…”

Section: B Operationalizationmentioning

confidence: 99%

An algebraic approach to temporal network analysis based on temporal quantities

Batagelj

Praprotnik

2016

Soc. Netw. Anal. Min.

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In a temporal network, the presence and activity of nodes and links can change through time. To describe temporal networks we introduce the notion of temporal quantities. We define the addition and multiplication of temporal quantities in a way that can be used for the definition of addition and multiplication of temporal networks. The corresponding algebraic structures are semirings. The usual approach to (data) analysis of temporal networks is to transform it into a sequence of time slices -static networks corresponding to selected time intervals and analyze each of them using standard methods to produce a sequence of results. The approach proposed in this paper enables us to compute these results directly. We developed fast algorithms for the proposed operations. They are available as an open source Python library TQ (Temporal Quantities) and a program Ianus. The proposed approach enables us to treat as temporal quantities also other network characteristics such as degrees, connectivity components, centrality measures, Pathfinder skeleton, etc. To illustrate the developed tools we present some results from the analysis of Franzosi's violence network and Corman's Reuters terror news network.

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Elementary models of dynamic networks

Cited by 10 publications

References 10 publications

Link removal for the control of stochastically evolving epidemics over networks: A comparison of approaches

Link removal for the control of stochastically evolving epidemics over networks: A comparison of approaches

Stream graphs and link streams for the modeling of interactions over time

An algebraic approach to temporal network analysis based on temporal quantities

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