Congestion Induced by the Structure of Multiplex Networks

Solé-Ribalta, Albert; Gómez, Sergio; Arenas, Àlex

doi:10.1103/physrevlett.116.108701

Cited by 131 publications

(91 citation statements)

References 25 publications

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“…References [34,35] provide more comprehensive reviews of this work. Approaches for detecting communities in multiplex networks are also relevant [36][37][38][39][40][41][42][43][44][45], as dynamic networks are a special case of multiplex networks, in which the layers are organized in a linear sequence. However, despite these varied efforts, up to now we have lacked a theoretical understanding of the optimality of these techniques, when or how they tend to fail, or whether there are fundamental limits to detecting community structure in dynamic networks.…”

Section: Introductionmentioning

confidence: 99%

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

et al. 2016

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The detection of communities within a dynamic network is a common means for obtaining a coarsegrained view of a complex system and for investigating its underlying processes. While a number of methods have been proposed in the machine learning and physics literature, we lack a theoretical analysis of their strengths and weaknesses, or of the ultimate limits on when communities can be detected. Here, we study the fundamental limits of detecting community structure in dynamic networks. Specifically, we analyze the limits of detectability for a dynamic stochastic block model where nodes change their community memberships over time, but where edges are generated independently at each time step. Using the cavity method, we derive a precise detectability threshold as a function of the rate of change and the strength of the communities. Below this sharp threshold, we claim that no efficient algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this threshold. The first uses belief propagation, which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the belief propagation equations. These results extend our understanding of the limits of community detection in an important direction, and introduce new mathematical tools for similar extensions to networks with other types of auxiliary information.

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Section: Introductionmentioning

confidence: 99%

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

et al. 2016

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“…These means that, in two-layer multiplex networks, shortest paths between two nodes may exist in just one layer, in the other layer, in a path with transfers (what we call multiplex paths), or in a combination of them (see figure 1). Consequently, any property depending on paths in multiplex networks must consider the concept of source and destination as being intrinsically different to that of nodes, such as in the calculation of centrality measures [22][23][24], the analysis of interdependence [30], the analysis of random walks [21], or the study of congestion [29]. The former definition of shortest paths in multiplex networks imposes the necessity of correctly computing their distribution and multiplicity.…”

Section: Shortest Paths In Multiplex Networkmentioning

confidence: 99%

“…If the capacity of some nodes to process these elements is lower than their incoming rate, congestion emerges [7]. In the general case of multiplex networks [29], it was shown that congestion appears when the injection rate per node, ρ, reaches a critical value ρ c :…”

Section: Congestion In Multiplex Networkmentioning

confidence: 99%

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Effect of shortest path multiplicity on congestion of multiplex networks

2019

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Shortest paths are representative of discrete geodesic distances in graphs, and many descriptors of networks depend on their counting. In multiplex networks, this counting is radically important to quantify the switch between layers and it has crucial implications in the transportation efficiency and congestion processes. Here we present a mathematical approach to the computation of the joint distribution of distance and multiplicity (degeneration) of shortest paths in multiplex networks, and exploit its relation to congestion processes. The results allow us to approximate semi-analytically the onset of congestion in multiplex networks as a function of the congestion of its layers.

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“…[5][6][7][8]-and dynamic processes [9], such as mobility on urban multiplexes. The latter-which is the focus of this contribution, see next Section-has been tackled only recently [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Resilience analytics: coverage and robustness in multi-modal transportation networks

2018

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A multi-modal transportation system of a city can be modeled as a multiplex network with different layers corresponding to different transportation modes. These layers include, but are not limited to, bus network, metro network, and road network. Formally, a multiplex network is a multilayer graph in which the same set of nodes are connected by different types of relationships. Intra-layer relationships denote the road segments connecting stations of the same transportation mode, whereas inter-layer relationships represent connections between different transportation modes within the same station. Given a multi-modal transportation system of a city, we are interested in assessing its quality or efficiency by estimating the coverage i.e., a portion of the city that can be covered by a random walker who navigates through it within a given time budget, or steps. We are also interested in the robustness of the whole transportation system which denotes the degree to which the system is able to withstand a random or targeted failure affecting one or more parts of it. Previous approaches proposed a mathematical framework to numerically compute the coverage in multiplex networks. However solutions are usually based on eigenvalue decomposition, known to be time consuming and hard to obtain in the case of large systems. In this work, we propose MUME, an efficient algorithm for Multi-modal Urban Mobility Estimation, that takes advantage of the special structure of the supra-Laplacian matrix of the transportation multiplex, to compute the coverage of the system. We conduct a comprehensive series of experiments to demonstrate the effectiveness and efficiency of MUME on both synthetic and real transportation networks of various cities such as Paris, London, New York and Chicago. A future goal is to use this experience to make projections for a fast growing city like Doha.

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Congestion Induced by the Structure of Multiplex Networks

Cited by 131 publications

References 25 publications

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

Effect of shortest path multiplicity on congestion of multiplex networks

Resilience analytics: coverage and robustness in multi-modal transportation networks

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