Topological relation of layered complex networks

Zou, Sheng-Rong; Ta, Zhou; Liu, Aifen; Xiao-li, XU; He, Daihai

doi:10.1016/j.physleta.2010.08.073

Cited by 33 publications

(19 citation statements)

References 22 publications

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“…Nevertheless, many systems are not formed by isolated networks, instead they are formed by a network of networks [7][8][9]. Examples include multimodal transportation networks [10,11], climatic systems [12], economic markets [13], energy-supply networks [14] and the human brain [15]. Moreover many networks are multiplex indicating the fact that two nodes can belong to different networks at the same time.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of multiplex networks: Entropy and overlap

2013

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There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplex are characterized by a significant overlap of the links in different layers. In this paper we introduce a statistical mechanics framework to describe multiplex ensembles. A multiplex is a system formed by N nodes and M layers of interactions where each node belongs to the M layers at the same time. Each layer α is formed by a network G α . Here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer. This implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers. Moreover we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplex in these ensembles. Finally we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes.

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Section: Introductionmentioning

confidence: 99%

Statistical mechanics of multiplex networks: Entropy and overlap

2013

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“…With the idea mentioned above, we may think that space P describes a kind of traffic flow while space L represents the information of the bus lines, which is the physical infrastructure of the flow [33] [34] . In fact, because of space L does not contain the case that two buses may run the same road but not share all their stations, it can't describe the road network exactly.…”

Section: The Model Of Layered Bus-transport Networkmentioning

confidence: 99%

Robustness Analysis of Layered Public Transport Networks Due to Edge Overload Breakdown

Dong¹,

Yang²,

Chen³

2014

IJITCS

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Abstract-The robustness of urban bus-transport networks has important influence on the network performance. This paper proposes the model of layered public bus-transport network which is composed of the logical layer and the physical layer and expounds the relationship between these two layers. We map the bustransport network into two spaces: space P and space L and take space P as logical layer while space L as physical layer. We define the load of edges in the physical layer according to the traffic flow in the logical layer and assume that a removed edge only leads to a redistribution of the load through it to its neighboring edges. We analysis the robustness of layered public bustransport networks in the face of cascading failure under the case of removing the edge with the highest load and redistributing of the load. Through the simulation of the public bus-transport networks of three major cities in China, we find that in the layered public bus-transport network the traffic flow in the logical layer affects the distribution of load of edges in the physical layer. The removal of the edge with the highest load may lead to the cascading failures of the physical layer, and the avalanche size decreases with the increase of the tolerance parameter.

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“…Representative types of multiplex networks range from social networks [1] and biological networks [2] to power grids [3] and transportation networks [4,5]. In multiplex networks, network layers are not isolated entities but interact with each other as an integrated system [6].…”

Section: Introductionmentioning

confidence: 99%

Understanding coupling dynamics of public transportation networks

et al. 2018

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Subway and bus networks work as an integrated multiplex transportation system and play an indispensable role in modern big cities. Even though a variety of works have investigated the coupling dynamics of multiplex transportation networks, empirical data that validates the determinant coupling factors are still lacking. In this paper, we employ smartcard data of 2.4 million subway and bus passengers in Shenzhen, China to study the coupling dynamics of subway and bus networks. Surprisingly, the coupling of subway and bus networks is not notably influenced by the time-varying speed ratio of the two network layers but is jointly determined by the distribution of travel demands and transportation facilities. Our findings highlight the important role of real travel demand data in analyzing the coupling dynamics of multiplex transportation networks. They also suggest that the speed ratio of different network layers, which was regarded as a key factor in determining coupling strength, has a negligible effect on travelers' route selections, and thus the coupling dynamics of multiplex transportation networks.

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Topological relation of layered complex networks

Cited by 33 publications

References 22 publications

Statistical mechanics of multiplex networks: Entropy and overlap

Statistical mechanics of multiplex networks: Entropy and overlap

Robustness Analysis of Layered Public Transport Networks Due to Edge Overload Breakdown

Understanding coupling dynamics of public transportation networks

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