Extraction and analysis of traffic and topologies of transportation networks

An Event-Link Network Model Based on Representation in P-Space

The L-space and P-space are two essential representations for studying complex networks that contain different clusters. Existing network models can successfully generate networks in L-space, but generating networks in P-space poses significant challenges. In this study, we present an empirical analysis of the distribution of the number of a line's nodes and the properties of the networks generated by these data in P-space. To gain insights into the operational mechanisms of the network of these data, we propose an event-link model that incorporates new nodes and links in P-space based on actual data characteristics using real data from marine and public transportation networks. The entire network consists of a series of events that consist of many nodes, and all nodes in an event are connected in the P-space. We conduct simulation experiments to explore the model's topological features under different parameter conditions, demonstrating that the simulation outcomes are consistent with the theoretical analysis of the model. This model exhibits small-world characteristics, scale-free behavior, and a high clustering coefficient. The event-link model, with its adjustable parameters, effectively generates networks with stable structures that closely resemble the statistical characteristics of real-world networks that share similar growth mechanisms. Moreover, the network's growth and evolution can be flexibly adjusted by modifying the model parameters.

An approach for accessibility assessment and vulnerability analysis of national multimodal transport systems

A series of ambitious accessibility-oriented policies have been launched in the world, which center around improving accessibility via the national multimodal transport systems including road, airline, and railway. The national multimodal transport accessibility assessment is one of the "basic" analyses for the design and implementation of these policies, whereas existing national-scale accessibility studies either focus on single-mode or two-mode transport or ignore the schedule-dependent nature of railway and airline. This article models the integrated road, railway, airline, and walking transport as a four-layer network with the consideration of their interdependencies. An algorithm is then developed to accurately assess the travel time-based accessibility on the four-layer network with the consideration of the daily schedule of trains and flights. The proposed approach is applied to map accessibility to 363 cities in mainland China and analyze the optimal travel modes. In addition, this article investigates the travel time-based vulnerability of the national multimodal transport system in mainland China under the extreme storm recently occurred in Zhengzhou (July 2021). The findings in this work provide insightful suggestions for transport planners to design the national multimodal transport systems and for stakeholders to schedule travels.

Inundation Resilience Analysis of Metro-Network from a Complex System Perspective Using the Grid Hydrodynamic Model and FBWM Approach: A Case Study of Wuhan

The upward trend of metro flooding disasters inevitably brings new challenges to urban underground flood management. It is essential to evaluate the resilience of metro systems so that efficient flood disaster plans for preparation, emergency response, and timely mitigation may be developed. Traditional response solutions merged multiple sources of data and knowledge to support decision-making. An obvious drawback is that original data sources for evaluations are often stationary, inaccurate, and subjective, owing to the complexity and uncertainty of the metro station’s actual physical environment. Meanwhile, the flood propagation path inside the whole metro station network was prone to be neglected. This paper presents a comprehensive approach to analyzing the resilience of metro networks to solve these problems. Firstly, we designed a simplified weighted and directed metro network module containing six characteristics by a topological approach while considering the slope direction between sites. Subsequently, to estimate the devastating effects and details of the flood hazard on the metro system, a 100-year rainfall–flood scenario simulation was conducted using high-precision DEM and a grid hydrodynamic model to identify the initially above-ground inundated stations (nodes). We developed a dynamic node breakdown algorithm to calculate the inundation sequence of the nodes in the weighted and directed network of the metro. Finally, we analyzed the resilience of the metro network in terms of toughness strength and organization recovery capacity, respectively. The fuzzy best–worst method (FBWM) was developed to obtain the weight of each assessment metric and determine the toughness strength of each node and the entire network. The results were as follows. (1) A simplified three-dimensional metro network based on a complex system perspective was established through a topological approach to explore the resilience of urban subways. (2) A grid hydrodynamic model was developed to accurately and efficiently identify the initially flooded nodes, and a dynamic breakdown algorithm realistically performed the flooding process of the subway network. (3) The node toughness strength was obtained automatically by a nonlinear FBWM method under the constraint of the minimum error to sustain the resilience assessment of the metro network. The research has considerable implications for managing underground flooding and enhancing the resilience of the metro network.

Dynamical efficiency for multimodal time-varying transportation networks

Spatial systems that experience congestion can be modeled as weighted networks whose weights dynamically change over time with the redistribution of flows. This is particularly true for urban transportation networks. The aim of this work is to find appropriate network measures that are able to detect critical zones for traffic congestion and bottlenecks in a transportation system. We propose for both single and multi-layered networks a path-based measure, called dynamical efficiency, which computes the travel time differences under congested and free-flow conditions. The dynamical efficiency quantifies the reachability of a location embedded in the whole urban traffic condition, in lieu of a myopic description based on the average speed of single road segments. In this way, we are able to detect the formation of congestion seeds and visualize their evolution in time as well-defined clusters. Moreover, the extension to multilayer networks allows us to introduce a novel measure of centrality, which estimates the expected usage of inter-modal junctions between two different transportation means. Finally, we define the so-called dilemma factor in terms of number of alternatives that an interconnected transportation system offers to the travelers in exchange for a small increase in travel time. We find macroscopic relations between the percentage of extra-time, number of alternatives and level of congestion, useful to quantify the richness of trip choices that a city offers. As an illustrative example, we show how our methods work to study the real network of a megacity with probe traffic data.

Measuring the effect of distance on the network topology of the Global Container Shipping Network

This paper examines how spatial distance affects network topology on empirical data concerning the Global Container Shipping Network (GCSN). The GCSN decomposes into 32 multiplex layers, defined at several spatial levels, by successively removing connections of smaller distances. This multilayer decomposition approach allows studying the topological properties of each layer as a function of distance. The analysis provides insights into the hierarchical structure and (importing and exporting) trade functionality of the GCSN, hub connectivity, several topological aspects, and the distinct role of China in the network's structure. It also shows that bidirectional links decrease with distance, highlighting the importance of asymmetric functionality in carriers' operations. It further configures six novel clusters of ports concerning their spatial coverage. Finally, it reveals three levels of geographical scale in the structure of GCSN (where the network topology significantly changes): the neighborhood (local connectivity); the scale of international connectivity (mesoscale or middle connectivity); and the intercontinental market (large scale connectivity). The overall approach provides a methodological framework for analyzing network topology as a function of distance, highlights the spatial dimension in complex and multilayer networks, and provides insights into the spatial structure of the GCSN, which is the most important market of the global maritime economy.

Spatiotemporal behaviors of the ridership of a public transportation system during an epidemic outbreak: case of MERS in Seoul

During May and June 2015, an outbreak of the Middle East respiratory syndrome (MERS) occurred in Korea, which raised the fear of contagion throughout society and suppressed the use of public transportation systems. Exploring daily ridership data of the Seoul bus transportation system, along with the number of infected patients and search volume in web portals, we observe that ridership decreased abruptly while attention was heavily focused online. Then this temporal reduction recovered exponentially with a characteristic time of 3 weeks when newly confirmed cases began to decrease. We also find with the data of ranked keywords of web portals that areas with severely reduced ridership tended to cluster and spatiotemporal variations of such clusters were highly associated with general hospitals where MERS patients were treated. On the other hand, the spatial reduction in ridership relaxed algebraically with the distance from a general hospital while the outbreak was severe. We further probe the influence of the epidemic outbreak in the framework of linear response theory, which relates the responses to the epidemic outbreak ("perturbation") with correlations in the absence of the perturbation. Indeed, the spatial correlation function of the ridership changes is observed to follow a power law, sharing the same exponent as the spatial relaxation of the response function. This new theoretical approach offers a useful tool for understanding responses of public transportation system to epidemic or accidental disasters.

Navigating optimal treaty-shopping routes using a multiplex network model

The international tax treaty system is a highly integrated and complex network. In this system, many multinational enterprises (MNEs) explore ways of reducing taxes by choosing optimal detour routes. Treaty abuse by these MNEs causes significant loss of tax revenues for many countries, but there is no systematic way of regulating their actions. However, it may be helpful to find a way of detecting the optimal routes by which MNEs avoid taxes and observe the effects of this behavior. In this paper, we investigate the international tax treaty network system of foreign investment channels based on real data and introduce a novel measure of tax-routing centrality and other centralities via network analysis. Our analysis of tax routing in a multiplex network reveals not only various tax-minimizing routes and their rates, but also new paths which cannot be found by navigating a single network layer. In addition, we identify strongly connected components of the multiplex tax treaty system with minimal tax shopping routes; more than 80 countries are included in this system. This means that there are far more pathways to be observed than can be detected on any given individual single layer. We provide a unified framework for analyzing the international tax treaty system and observing the effects of tax avoidance by MNEs.

Topological Structure and Robustness of the Lymph Node Conduit System

Fibroblastic reticular cells (FRCs) form a road-like cellular network in lymph nodes (LNs) that provides essential chemotactic, survival, and regulatory signals for immune cells. While the topological characteristics of the FRC network have been elaborated, the network properties of the micro-tubular conduit system generated by FRCs, which drains lymph fluid through a pipeline-like system to distribute small molecules and antigens, has remained unexplored. Here, we quantify the crucial 3D morphometric parameters and determine the topological properties governing the structural organization of the intertwined networks. We find that the conduit system exhibits lesser small-worldness and lower resilience to perturbation compared to the FRC network, while the robust topological organization of both networks is maintained in a lymphotoxin-β-receptor-independent manner. Overall, the high-resolution topological analysis of the "roads-and-pipes" networks highlights essential parameters underlying the functional organization of LN micro-environments and will, hence, advance the development of multi-scale LN models.

StationRank: Aggregate dynamics of the Swiss railway

Increasing availability and quality of actual, as opposed to scheduled, open transport data offers new possibilities for capturing the spatiotemporal dynamics of railway and other networks of social infrastructure. One way to describe such complex phenomena is in terms of stochastic processes. At its core, a stochastic model is domain-agnostic and algorithms discussed here have been successfully used in other applications, including Google’s PageRank citation ranking. Our key assumption is that train routes constitute meaningful sequences analogous to sentences of literary text. A corpus of routes is thus susceptible to the same analytic tool-set as a corpus of sentences. With our experiment in Switzerland, we introduce a method for building Markov Chains from aggregated daily streams of railway traffic data. The stationary distributions under normal and perturbed conditions are used to define systemic risk measures with non-evident, valuable information about railway infrastructure.

Network Characteristics and Vulnerability Analysis of Chinese Railway Network under Earthquake Disasters

The internal structure and operation rules of railway network have become increasingly complex along with the expansion of the network, putting a higher demand on the development of the railway and the reliability and adaptability of the railway under earthquake disasters. The theory and method concerning complex railway network can well capture the internal structure of railway facilities system and the relationship between subsystems. However, most of the research focuses on the vulnerability based on the logical network of railway, deviating from the actual spatial location of railway network. Additionally, only random attacks and deliberate attacks are factored in, ignoring the impact of earthquake disasters on actual railway lines. Therefore, this paper built a geographic railway network and analyzed topological structure of the network and its vulnerability under earthquake disasters. First, the geographic network of Chinese railway was built based on the methods of complex network, linear reference and dynamic segmentation. Second, the spatial distribution of railway network flow was analyzed by node degree, betweenness and clustering coefficient. Finally, the vulnerability of the geographic railway network in areas with high seismic hazards were assessed, aiming to improve the capacity to prevent and resist earthquake disasters.

Does China's high-speed rail development lead to regional disparities? A network perspective

This research examines whether cities are getting more equally accessible and connected via high-speed rail (HSR) in China over the period from 2010 to 2015. Existing studies mainly use network centralities to describe the spatial pattern of HSR network without measuring the spatial disparity of these centralities, and most of them rely on the infrastructure network and thus fail to incorporate HSR service quality in the centrality measures. Using HSR timetable data, we incorporate both scheduled travel time and daily frequency of each origin-destination city pair into three centrality measures and further quantify their inequalities using Theil's T index. We find that as the HSR network expands, cities appear to be more equal in terms of accessibility, but their disparities in connectivity and transitivity depend on the dimensions of comparison. In general, although the difference between economic regions or between megalopolises has reduced, small/medium-sized cities not belonging to any major city cluster are further lagged behind in HSR development. The difference between core and non-core cities in the same megalopolises has decreased despite that non-core cities are increasingly relying on core cities to access other regions.

A Method of Bus Network Optimization Based on Complex Network and Beidou Vehicle Location

Aiming at the problems of poor time performance and accuracy in bus stops network optimization, this paper proposes an algorithm based on complex network and graph theory and Beidou Vehicle Location to measure the importance of bus stops. This method narrows the scope of points and edges to be optimized and is applied to the Jinan bus stop network. In this method, the bus driving efficiency, which can objectively reflect actual road conditions, is taken as the weight of the connecting edges in the network, and the network is optimized through the network efficiency. The experimental results show that, compared with the original network, the optimized network time performance is good and the optimized network bus driving efficiency is improved.

Hierarchical structure in the world's largest high-speed rail network

Presently, China has the largest high-speed rail (HSR) system in the world. However, our understanding of the network structure of the world's largest HSR system remains largely incomplete due to the limited data available. In this study, a publicly available data source, namely, information from a ticketing website, was used to collect an exhaustive dataset on the stations and routes within the Chinese HSR system. The dataset included all 704 HSR stations that had been built as of June, 2016. A classical set of frequently used metrics based on complex network theory were analyzed, including degree centrality, betweenness centrality, and closeness centrality. The frequency distributions of all three metrics demonstrated highly consistent bimodal-like patterns, suggesting that the Chinese HSR network consists of two distinct regimes. The results indicate that the Chinese HSR system has a hierarchical structure, rather than a scale-free structure as has been commonly observed. To the best of our knowledge, such a network structure has not been found in other railway systems, or in transportation systems in general. Follow-up studies are needed to reveal the formation mechanisms of this hierarchical network structure.

Critical Infrastructure Vulnerability to Spatially Localized Failures with Applications to Chinese Railway System

This article studies a general type of initiating events in critical infrastructures, called spatially localized failures (SLFs), which are defined as the failure of a set of infrastructure components distributed in a spatially localized area due to damage sustained, while other components outside the area do not directly fail. These failures can be regarded as a special type of intentional attack, such as bomb or explosive assault, or a generalized modeling of the impact of localized natural hazards on large-scale systems. This article introduces three SLFs models: node centered SLFs, district-based SLFs, and circle-shaped SLFs, and proposes a SLFs-induced vulnerability analysis method from three aspects: identification of critical locations, comparisons of infrastructure vulnerability to random failures, topologically localized failures and SLFs, and quantification of infrastructure information value. The proposed SLFs-induced vulnerability analysis method is finally applied to the Chinese railway system and can be also easily adapted to analyze other critical infrastructures for valuable protection suggestions.

Exploring the Hierarchical Structure of China’s Railway Network from 2008 to 2017

The analysis of transport networks is an important component of urban and regional development and planning. Based on the four main stages of China’s railway development from 2008 to 2017, this paper analyzes the hierarchical and spatial heterogeneity distribution of train flows. We found a high degree of spatial matching with the distribution of China’s main railway corridors. Then, using a classical community detection algorithm, this paper attempts to describe the functional structure and regional effects of China’s railway network. We also explore the impacts of construction policies and changes to train operations on the spatial organizing pattern and evolution of network hierarchies. The results of this empirical study reveal a clear pattern of independent communities, which in turn indicates the existence of a hierarchical structure in China’s railway network. The decreases in both the number of communities and average distance between community centers indicate that the newer high-speed rail services have shortened the connections between cities. In addition, the detected communities are inconsistent with China’s actual administrative divisions in terms of quantity and boundaries. The spatial spillover and segmentation effects cause the railway network in different regions to be self-contained. Finally, the detected communities in each stage can be divided into the categories of monocentric structure, dual-nuclei structure, and polycentric structure according to the number of extracted hubs. The polycentric structure is the dominant mode, which shows that the railway network has significant spatial dependence and a diversified spatial organization mode. This study has great significance for policymakers seeking to guide the future construction of high-speed rail lines and optimize national or regional railway networks.

Comparing two classes of biological distribution systems using network analysis

Distribution networks-from vasculature to urban transportation pathways-are spatially embedded networks that must route resources efficiently in the face of pressures induced by the costs of building and maintaining network infrastructure. Such requirements are thought to constrain the topological and spatial organization of these systems, but at the same time, different kinds of distribution networks may exhibit variable architectural features within those general constraints. In this study, we use methods from network science to compare and contrast two classes of biological transport networks: mycelial fungi and vasculature from the surface of rodent brains. These systems differ in terms of their growth and transport mechanisms, as well as the environments in which they typically exist. Though both types of networks have been studied independently, the goal of this study is to quantify similarities and differences in their network designs. We begin by characterizing the structural backbone of these systems with a collection of measures that assess various kinds of network organization across topological and spatial scales, ranging from measures of loop density, to those that quantify connected pathways between different network regions, and hierarchical organization. Most importantly, we next carry out a network analysis that directly considers the spatial embedding and properties especially relevant to the function of distribution systems. We find that although both the vasculature and mycelia are highly constrained planar networks, there are clear distinctions in how they balance tradeoffs in network measures of wiring length, efficiency, and robustness. While the vasculature appears well organized for low cost, but relatively high efficiency, the mycelia tend to form more expensive but in turn more robust networks. As a whole, this work demonstrates the utility of network-based methods to identify both common features and variations in the network structure of different classes of biological transport systems.

Exploring Railway Network Dynamics in China from 2008 to 2017

China’s high speed rail (HSR) network has been rapidly constructed and developed during the past 10 years. However, few studies have reported the spatiotemporal changes of railway network structures and how those structures have been affected by the operation of high speed rail systems in different periods. This paper analyzes the evolving network characteristics of China’s railway network during each of the four main stages of HSR development over a 10-year period. These four stages include Stage 1, when no HSR was in place prior to August 2008; Stage 2, when several HSR lines were put into operation between August 2008, and July 2011; Stage 3, when the network skeleton of most main HSR lines was put into place. This covered the period until January 2013. Finally, Stage 4 covers the deep intensification of several new HSR lines and the rapid development of intercity-HSR railway lines between January 2013, and July 2017. This paper presents a detailed analysis of the timetable-based statistical properties of China’s railway network, as well as the spatiotemporal patterns of the more than 2700 stations that have been affected by the opening of HSR lines and the corresponding policy changes. Generally, we find that the distribution of both degrees and strengths are characterized by scale-free patterns. In addition, the decreasing average path length and increasing network clustering coefficient indicate that the small world characteristic is more significant in the evolution of China’s railway network. Correlations between different network indices are explored, in order to further investigate the dynamics of China’s railway system. Overall, our study offers a new approach for assessing the growth and evolution of a real railway network based on train timetables. Our study can also be referenced by policymakers looking to adjust HSR operations and plan future HSR routes.

Applying network theory to animal movements to identify properties of landscape space use

Network (graph) theory is a popular analytical framework to characterize the structure and dynamics among discrete objects and is particularly effective at identifying critical hubs and patterns of connectivity. The identification of such attributes is a fundamental objective of animal movement research, yet network theory has rarely been applied directly to animal relocation data. We develop an approach that allows the analysis of movement data using network theory by defining occupied pixels as nodes and connection among these pixels as edges. We first quantify node-level (local) metrics and graph-level (system) metrics on simulated movement trajectories to assess the ability of these metrics to pull out known properties in movement paths. We then apply our framework to empirical data from African elephants (Loxodonta africana), giant Galapagos tortoises (Chelonoidis spp.), and mule deer (Odocoileous hemionus). Our results indicate that certain node-level metrics, namely degree, weight, and betweenness, perform well in capturing local patterns of space use, such as the definition of core areas and paths used for inter-patch movement. These metrics were generally applicable across data sets, indicating their robustness to assumptions structuring analysis or strategies of movement. Other metrics capture local patterns effectively, but were sensitive to specified graph properties, indicating case specific applications. Our analysis indicates that graph-level metrics are unlikely to outperform other approaches for the categorization of general movement strategies (central place foraging, migration, nomadism). By identifying critical nodes, our approach provides a robust quantitative framework to identify local properties of space use that can be used to evaluate the effect of the loss of specific nodes on range wide connectivity. Our network approach is intuitive, and can be implemented across imperfectly sampled or large-scale data sets efficiently, providing a framework for conservationists to analyze movement data. Functions created for the analyses are available within the R package moveNT.

Pendular behavior of public transport networks

In this paper, we propose a methodology that bears close resemblance to the Fourier analysis of the first harmonic to study networks subjected to pendular behavior. In this context, pendular behavior is characterized by the phenomenon of people's dislocation from their homes to work in the morning and people's dislocation in the opposite direction in the afternoon. Pendular behavior is a relevant phenomenon that takes place in public transport networks because it may reduce the overall efficiency of the system as a result of the asymmetric utilization of the system in different directions. We apply this methodology to the bus transport system of Brasília, which is a city that has commercial and residential activities in distinct boroughs. We show that this methodology can be used to characterize the pendular behavior of this system, identifying the most critical nodes and times of the day when this system is in more severe demanded.

Visually Exploring Transportation Schedules

Public transportation schedules are designed by agencies to optimize service quality under multiple constraints. However, real service usually deviates from the plan. Therefore, transportation analysts need to identify, compare and explain both eventual and systemic performance issues that must be addressed so that better timetables can be created. The purely statistical tools commonly used by analysts pose many difficulties due to the large number of attributes at trip- and station-level for planned and real service. Also challenging is the need for models at multiple scales to search for patterns at different times and stations, since analysts do not know exactly where or when relevant patterns might emerge and need to compute statistical summaries for multiple attributes at different granularities. To aid in this analysis, we worked in close collaboration with a transportation expert to design TR-EX, a visual exploration tool developed to identify, inspect and compare spatio-temporal patterns for planned and real transportation service. TR-EX combines two new visual encodings inspired by Marey's Train Schedule: Trips Explorer for trip-level analysis of frequency, deviation and speed; and Stops Explorer for station-level study of delay, wait time, reliability and performance deficiencies such as bunching. To tackle overplotting and to provide a robust representation for a large numbers of trips and stops at multiple scales, the system supports variable kernel bandwidths to achieve the level of detail required by users for different tasks. We justify our design decisions based on specific analysis needs of transportation analysts. We provide anecdotal evidence of the efficacy of TR-EX through a series of case studies that explore NYC subway service, which illustrate how TR-EX can be used to confirm hypotheses and derive new insights through visual exploration.

The multilayer temporal network of public transport in Great Britain

Despite the widespread availability of information concerning public transport coming from different sources, it is extremely hard to have a complete picture, in particular at a national scale. Here, we integrate timetable data obtained from the United Kingdom open-data program together with timetables of domestic flights, and obtain a comprehensive snapshot of the temporal characteristics of the whole UK public transport system for a week in October 2010. In order to focus on multi-modal aspects of the system, we use a coarse graining procedure and define explicitly the coupling between different transport modes such as connections at airports, ferry docks, rail, metro, coach and bus stations. The resulting weighted, directed, temporal and multilayer network is provided in simple, commonly used formats, ensuring easy access and the possibility of a straightforward use of old or specifically developed methods on this new and extensive dataset.

Anatomy and efficiency of urban multimodal mobility

The growth of transportation networks and their increasing interconnections, although positive, has the downside effect of an increasing complexity which make them difficult to use, to assess, and limits their efficiency. On average in the UK, 23% of travel time is lost in connections for trips with more than one mode, and the lack of synchronization decreases very slowly with population size. This lack of synchronization between modes induces differences between the theoretical quickest trip and the 'time-respecting' path, which takes into account waiting times at interconnection nodes. We analyse here the statistics of these paths on the multilayer, temporal network of the entire, multimodal british public transportation system. We propose a statistical decomposition - the 'anatomy' - of trips in urban areas, in terms of riding, waiting and walking times, and which shows how the temporal structure of trips varies with distance and allows us to compare different cities. Weaknesses in systems can be either insufficient transportation speed or service frequency, but the key parameter controlling their global efficiency is the total number of stop events per hour for all modes. This analysis suggests the need for better optimization strategies, adapted to short, long unimodal or multimodal trips.

Robustness elasticity in complex networks

Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems.

Exploring maps with greedy navigators

During the last decade of network research focusing on structural and dynamical properties of networks, the role of network users has been more or less underestimated from the bird's-eye view of global perspective. In this era of global positioning system equipped smartphones, however, a user's ability to access local geometric information and find efficient pathways on networks plays a crucial role, rather than the globally optimal pathways. We present a simple greedy spatial navigation strategy as a probe to explore spatial networks. These greedy navigators use directional information in every move they take, without being trapped in a dead end based on their memory about previous routes. We suggest that the centralities measures have to be modified to incorporate the navigators' behavior, and present the intriguing effect of navigators' greediness where removing some edges may actually enhance the routing efficiency, which is reminiscent of Braess's paradox. In addition, using samples of road structures in large cities around the world, it is shown that the navigability measure we define reflects unique structural properties, which are not easy to predict from other topological characteristics. In this respect, we believe that our routing scheme significantly moves the routing problem on networks one step closer to reality, incorporating the inevitable incompleteness of navigators' information.

Error and attack tolerance of layered complex networks

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.

Geographical networks evolving with an optimal policy

In this article we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a node, having randomly assigned coordinates in a 1x1 square, is added and connected to a previously existing node i, which minimizes the quantity ri2/kialpha, where ri is the geographical distance, ki the degree, and alpha a free parameter. The degree distribution obeys a power-law form when alpha=1, and an exponential form when alpha=0. When alpha is in the interval (0, 1), the network exhibits a stretched exponential distribution. We prove that the average topological distance increases in a logarithmic scale of the network size, indicating the existence of the small-world property. Furthermore, we obtain the geographical edge length distribution, the total geographical length of all edges, and the average geographical distance of the whole network. Interestingly, we found that the total edge length will sharply increase when alpha exceeds the critical value alphac=1, and the average geographical distance has an upper bound independent of the network size. All the results are obtained analytically with some reasonable approximations, which are well verified by simulations.