Vulnerability and protection of infrastructure networks

Cross-Frequency Multilayer Network Analysis with Bispectrum-based Functional Connectivity: A Study of Alzheimer's Disease

Alzheimer's disease (AD) is a neurodegenerative disorder known to affect functional connectivity (FC) across many brain regions. Linear FC measures have been applied to study the differences in AD by splitting neurophysiological signals, such as electroencephalography (EEG) recordings, into discrete frequency bands and analysing them in isolation from each other. We address this limitation by quantifying cross-frequency FC in addition to the traditional within-band approach. Cross-bispectrum, a higher-order spectral analysis approach, is used to measure the nonlinear FC and is compared with the cross-spectrum, which only measures the linear FC within bands. This work reports the reconstruction of a cross-frequency FC network where each frequency band is treated as a layer in a multilayer network with both inter- and intra-layer edges. Cross-bispectrum detects cross-frequency differences, mainly increased FC in AD cases in δ-θ coupling. Overall, increased strength of low-frequency coupling and decreased level of high-frequency coupling is observed in AD cases in comparison to healthy controls (HC). We demonstrate that a graph-theoretic analysis of cross-frequency brain networks is crucial to obtain a more detailed insight into their structure and function. Vulnerability analysis reveals that the integration and segregation properties of networks are enabled by different frequency couplings in AD networks compared to HCs. Finally, we use the reconstructed networks for classification. The extra cross-frequency coupling information can improve the classification performance significantly, suggesting an important role of cross-frequency FC. The results highlight the importance of studying nonlinearity and including cross-frequency FC in characterising AD.

A perturbation-based approach to identifying potentially superfluous network constituents

Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.

Power-grid vulnerability and its relation with network structure

Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.

Invulnerability of the Urban Agglomeration Integrated Passenger Transport Network under Emergency Events

Urgent natural environmental events, such as floods, power failures, and epidemics, result in disruptions to the traffic system and heavy disturbances in public requirements. In order to strengthen the ability of the transport network to handle urgent natural environmental issues, this paper simulates the disruption situation of traffic stations in the urban agglomeration by attacking nodes, and evaluates the ability of the transport network to resist disruptions (i.e., invulnerability). Firstly, the model of the urban agglomeration integrated passenger transport network is established based on complex network theory. The highway network, railway network, and coupling network are combined into a multi-layer network space structure, and the edge weight is calibrated by travel time and cost. Secondly, the invulnerability simulation process including multiple attack modes under random and deliberate attack strategies is sorted out. By improving the traditional network efficiency indicator, the network impedance efficiency indicator is proposed to measure network performance, and the network relative impedance efficiency indicator is used to evaluate network invulnerability and identify key nodes. Finally, Chengdu-Chongqing urban agglomeration is taken as a case study. The results show that the network does not collapse quickly and it shows certain invulnerability and robustness under continuous random attacks. Network performance and invulnerability are not necessarily positively correlated. The failure of individual nodes that are small in scale but act as transit hubs may significantly degrade the network performance. The identified key nodes have significance for guiding the construction, maintenance, and optimization of the urban agglomeration passenger transport network, which is conducive to promoting public safety.

Mapping carbon emissions of China's domestic air passenger transport: From individual cities to intercity networks

As a significant carbon emission source with high growth potential, the air transport sector plays a crucial role in China's decarbonisation efforts. However, the spatial pattern and evolutionary dynamics of aviation carbon emissions in China have not been thoroughly studied. This study proposed a framework to reveal the spatial characteristics and influencing factors of aviation carbon emissions at the city level. Using data from 2019 to construct the aviation carbon emissions network of China (ACENC), the novelty of the study lies in the subdivision of carbon emissions of air passenger transport into cities and intercity lines in China, which helps to reveal the spatial characteristics of individual cities in the intercity network. Beijing, Shanghai, Shenzhen, Chengdu, and Guangzhou were the cities with the highest carbon emissions, and the routes between these cities caused a significant amount of carbon emissions. >80 % of the total carbon emissions can be attributed to two communities in the network, owing to their large size and strong connections. Correlation analysis indicates that a city's carbon emissions are significantly related to its demographic and economic attributes as well as its connection with other cities, while a city's carbon emission intensity may be influenced by its centrality in the whole network and the structure of the community to which it belongs. Overall, the presented results provide directions for stakeholders and policymakers to regulate carbon emissions from air transportation.

Decreasing distance from tumor to the language network causes language deficit

Preoperative language deficits are associated with alterations in the language networks of patients with gliomas. This study investigated how gliomas affect language performance by altering the language network. Ninety patients with lower-grade gliomas were included, and their preoperative language performance was evaluated using the Western Aphasia Battery. We also calculated the topological properties based on resting state functional magnetic resonance imaging. All patients were classified according to aphasia quotient (AQ) into the aphasia (AQ < 93.8), mild anomia (AQ > 93.8 and naming section <9.8), and normal groups (AQ > 93.8). The shortest distance from the tumor to the language network (SDTN) was evaluated to identify the effect on language performance induced by the tumor. One-way analysis of variance and post hoc analysis with Sidak correction were used to analyze the differences in topological properties among the three groups. Causal mediation analysis was used to identify indirectly affected mediators. Compared with the mild anomia group, longer shortest path length (p = .0016), lower vulnerability (p = .0331), and weaker nodal efficiencies of three nodes (right caudal Brodmann area [BA] 45, right caudal BA 22, and left BA 41/42, all p < .05) were observed in the aphasia group. The SDTN mediated nodal degree centrality and nodal vulnerability (left rostroventral BA 39), which negatively affected the AQs. Conventional language eloquent and mirrored areas participated in the language network alterations induced by gliomas. The SDTN was a mediator that affected the preoperative language status in patients with gliomas.

Topology Analysis of Natural Gas Pipeline Networks Based on Complex Network Theory

With the improvement of natural gas network interconnection, the network topology becomes increasingly complex. The significance of analyzing topology is gradually becoming prominent, and a systematic analysis method is required. This paper selects two typical natural gas pipeline networks: one in Europe, and the other in North China. Based on complex network theory and the nature of natural gas pipelines, topological models for the two typical networks were established and the evaluation indexes were developed based on four factors: network type, overall topological structure characteristics, path-related topological structure characteristics, and topological structure robustness. Using these indexes, the topological structure of the two typical networks is compared and analyzed quantitatively. The comparison shows that the European network topology has more redundancy, higher transmission efficiency, and greater robustness. The topology analysis method proposed in this paper is practical and suitable for the preliminary analysis of natural gas pipeline networks. The conclusions achieved by this method can assist operators in gaining an intuitive understanding of the overall characteristics, robustness, and key features of pipeline network topology, which is useful in the implementation of hierarchical prevention and control. It also serves as a solid theoretical foundation and guidance for network expansion, interconnection construction, and precise hydraulic simulation calculation in the next stage.

Increasing nodal vulnerability and nodal efficiency implied recovery time prolonging in patients with supplementary motor area syndrome

Supplementary motor area (SMA) syndrome is a surgery‐related complication that commonly occurs after removing SMA glioma, and needs weeks to recover. However, susceptible factors of patients suffering from SMA syndrome remain unknown. Graphic theory was applied to reveal topological properties of sensorimotor network (SMN) by processing resting‐state functional magnetic resonance images in 66 patients with SMA gliomas. Patients were classified into SMA and non‐SMA groups based on whether they suffered from SMA syndrome. We collected recovery time and used causal mediation analysis to find association between topological properties and recovery time. Compared with the non‐SMA group, higher vulnerability (left: p = .0018; right: p = .0033) and lower fault tolerance (left: p = .0022; right: p = .0248) of the whole SMN were found in the SMA group. Moreover, higher nodal properties of lesional‐hemispheric cingulate cortex (nodal efficiency: left, p = .0389; right, p = .0169; nodal vulnerability: left, p = .0185; right, p = .0085) and upper limb region of primary motor cortex (PMC; nodal efficiency: left, p = .0132; right, p = .0001; nodal vulnerability: left, p = .0091; right, p = .0209) were found in the SMA group. Nodal efficiency and nodal vulnerability of cingulate cortex and upper limb region of PMC were important predictors for SMA syndrome occurring and recovery time prolonging. Neurosurgeons should carefully deal with upper limb region of PMC and cingulate cortex, and protect them if these two region were unnecessary to damage during SMA glioma resection.

Contralesional Sensorimotor Network Participates in Motor Functional Compensation in Glioma Patients

Background

Some gliomas in sensorimotor areas induce motor deficits, while some do not. Cortical destruction and reorganization contribute to this phenomenon, but detailed reasons remain unclear. This study investigated the differences of the functional connectivity and topological properties in the contralesional sensorimotor network (cSMN) between patients with motor deficit and those with normal motor function.

Methods

We retrospectively reviewed 65 patients (32 men) between 2017 and 2020. The patients were divided into four groups based on tumor laterality and preoperative motor status (deficit or non-deficit). Thirty-three healthy controls (18 men) were enrolled after matching for sex, age, and educational status. Graph theoretical measurement was applied to reveal alterations of the topological properties of the cSMN by analyzing resting-state functional MRI.

Results

The results for patients with different hemispheric gliomas were similar. The clustering coefficient, local efficiency, transitivity, and vulnerability of the cSMN significantly increased in the non-deficit group and decreased in the deficit group compared to the healthy group (p < 0.05). Moreover, the nodes of the motor-related thalamus showed a significantly increased nodal efficiency and nodal local efficiency in the non-deficit group and decreased in the deficit group compared with the healthy group (p < 0.05).

Conclusions

We posited the existence of two stages of alterations of the preoperative motor status. In the compensatory stage, the cSMN sacrificed stability to acquire high efficiency and to compensate for impaired motor function. With the glioma growing and the motor function being totally damaged, the cSMN returned to a stable state and maintained healthy hemispheric motor function, but with low efficiency.

Common network effect-patterns after monoamine reuptake inhibition in dissociated hippocampus cultures

The pharmacological treatment of major depressive disorder with currently available antidepressant drugs is still unsatisfying as response to medication is delayed and in some patients even non-existent. To understand complex psychiatric diseases such as major depressive disorder and their treatment, research focus is shifting from investigating single neurons towards a view of the entire functional and effective neuronal network, because alterations on single synapses through antidepressant drugs may translate to alterations in the entire network. Here, we examined the effects of monoamine reuptake inhibitors on in vitro hippocampal network dynamics using calcium fluorescence imaging and analyzing the data with means of graph theoretical parameters. Hypothesizing that monoamine reuptake inhibitors operate through changes of effective connectivity on micro-scale neuronal networks, we measured the effects of the selective monoamine reuptake inhibitors GBR-12783, Sertraline, Venlafaxine, and Amitriptyline on neuronal networks. We identified a common pattern of effects of the different tested monoamine reuptake inhibitors. After treatment with GBR-12783, Sertraline, and Venlafaxine, the connectivity degree, measuring the number of existing connections in the network, was significantly decreased. All tested substances led to networks with more submodules and a reduced global efficiency. No monoamine reuptake inhibitor did affect network-wide firing rate, the characteristic path length, or the network strength. In our study, we found that monoamine reuptake inhibition in neuronal networks in vitro results in a sharpening of the network structure. These alterations could be the basis for the reorganization of a large-scale miswired network in major depressive disorder.

A network analysis of crab metamorphosis and the hypothesis of development as a process of unfolding of an intensive complexity

Development has intrigued humanity since ancient times. Today, the main paradigm in developmental biology and evolutionary developmental biology (evo-devo) is the genetic program, in which development is explained by the interplay and interaction of genes, that is, by the action of gene regulatory networks (GRNs). However, it is not even clear that a GRN, no matter how complex, can be translated into a form. Therefore, the fundamental enigma of development still remains: how is a complex organism formed from a single cell? This question unfolded the historical drama and the dialectical tension between preformation and epigenesis. In order to shed light on these issues, I studied the development of crabs (infraorder Brachyura), as representative of the subphylum Crustacea, using network theory. The external morphology of the different phases of brachyuran metamorphosis were modeled as networks and their main characteristics analyzed. As one could expect, the parameters usually regarded as indicative of network complexity, such as modularity and hierarchy, increased during development. However, when more sophisticated complexity measures were tested, it was evidenced that whereas a group of complexity measures increased during development, another group decreased. This led to consider that two kinds of complexities were being measured. I called them intensive and extensive complexity. In view of these results, I propose that crab development involves a passage from an intensive to an extensive complexity. In other words, crab development can be interpreted as a process of unfolding of an intensive, preexistent complexity.

Epilepsy enhance global efficiency of language networks in right temporal lobe gliomas

AIMS

We analyzed the resting state functional magnetic resonance images to investigate the alterations of neural networks in patients with glioma-related epilepsy (GRE).

METHODS

Fifty-six patients with right temporal lower-grade glioma were divided into GRE (n = 28) and non-GRE groups. Twenty-eight healthy subjects were recruited after matching age, sex, and education level. Sensorimotor, visual, language, and left executive control networks were applied to generate functional connectivity matrices, and their topological properties were investigated.

RESULTS

No significant alterations in functional connectivity were found. The least significant discovery test revealed differences only in the language network. The shortest path length, clustering coefficient, local efficiency, and vulnerability were greater in the non-GRE group than in the other groups. The nodal efficiencies of two nodes (mirror areas to Broca and Wernicke) were weaker in the non-GRE group than in the other groups. The node of degree centrality (Broca), nodal local efficiency (Wernicke), and nodal clustering coefficient (temporal polar) were greater in the non-GRE group than in the healthy group.

CONCLUSION

Different tumor locations alter different neural networks. Temporal lobe gliomas in the right hemisphere altered the language network. Glioma itself and GRE altered the network in opposing ways in patients with right temporal glioma.

Percolation of heterogeneous flows uncovers the bottlenecks of infrastructure networks

Whether it be the passengers’ mobility demand in transportation systems, or the consumers’ energy demand in power grids, the primary purpose of many infrastructure networks is to best serve this flow demand. In reality, the volume of flow demand fluctuates unevenly across complex networks while simultaneously being hindered by some form of congestion or overload. Nevertheless, there is little known about how the heterogeneity of flow demand influences the network flow dynamics under congestion. To explore this, we introduce a percolation-based network analysis framework underpinned by flow heterogeneity. Thereby, we theoretically identify bottleneck links with guaranteed decisive impact on how flows are passed through the network. The effectiveness of the framework is demonstrated on large-scale real transportation networks, where mitigating the congestion on a small fraction of the links identified as bottlenecks results in a significant network improvement.

Infrastructure networks are characterized by fluctuations of flow demand between different points and temporal congestion or overload on flow pathways. Hamedmoghadam et al. identify congestion bottlenecks in networks relevant to communication, transportation, water supply, and power distribution.

Recovery patterns and physics of the network

In a progressively interconnected world, the loss of system resilience has consequences for human health, the economy, and the environment. Research has exploited the science of networks to explain the resilience of complex systems against random attacks, malicious attacks, and the localized attacks induced by natural disasters or mass attacks. Little is known about the elucidation of system recovery by the network topology. This study adds to the knowledge of network resilience by examining the nexus of recoverability and network topology. We establish a new paradigm for identifying the recovery behavior of networks and introduce the recoverability measure. Results indicate that the recovery response behavior and the recoverability measure are the function of both size and topology of networks. In small sized networks, the return to recovery exhibits homogeneous recovery behavior over topology, while the return shape is dispersed with an increase in the size of network. A network becomes more recoverable as connectivity measures of the network increase, and less recoverable as accessibility measures of network increase. Overall, the results not only offer guidance on designing recoverable networks, but also depict the recovery nature of networks deliberately following a disruption. Our recovery behavior and recoverability measure has been tested on 16 distinct network topologies. The relevant recovery behavior can be generalized based on our definition for any network topology recovering deliberately.

Epidemic spreading and control strategies in spatial modular network

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the susceptible-infected-recovered model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.

Epilepsy-Related Brain Network Alterations in Patients With Temporal Lobe Glioma in the Left Hemisphere

Background: Seizures are a common symptom in patients with temporal lobe gliomas and may result in brain network alterations. However, brain network changes caused by glioma-related epilepsy (GRE) remain poorly understood. Objective: In this study, we applied graph theory analysis to delineate topological networks with resting-state functional magnetic resonance images (rs-fMRI) and investigated characteristics of functional networks in patients with GRE. Methods: Thirty patients with low-grade gliomas in the left temporal lobe were enrolled and classified into GRE (n = 15) and non-GRE groups. Twenty healthy participants matched for age, sex, and education level were enrolled. All participants had rs-fMRI data. Sensorimotor, visual, default mode, auditory, and right executive control networks were used to construct connection matrices. Topological properties of those sub-networks were investigated. Results: Compared to that in the GRE group, four edges with higher functional connectivity were noted in the non-GRE group. Moreover, 21 edges with higher functional connectivity were identified in the non-GRE group compared to the healthy group. All significant alterations in functional edges belong to the visual network. Increased global efficiency and decreased shortest path lengths were noted in the non-GRE group compared to the GRE and healthy groups. Compared with that in the healthy group, nodal efficiency of three nodes was higher in the GRE and non-GRE groups and the degree centrality of six nodes was altered in the non-GRE group. Conclusion: Temporal lobe gliomas in the left hemisphere and GRE altered visual networks in an opposing manner. These findings provide a novel insight into brain network alterations induced by GRE.

An asymmetric interdependent networks model for cyber-physical systems

Cyber-physical systems (CPSs) are integrations of information technology and physical systems, which are more and more significant in society. As a typical example of CPSs, smart grids integrate many advanced devices and information technologies to form a safer and more efficient power system. However, interconnection with the cyber network makes the system more complex, so that the robustness assessment of CPSs becomes more difficult. This paper proposes a new CPS model from a complex network perspective. We try to consider the real dynamics of cyber and physical parts and the asymmetric interdependency between them. Simulation results show that coupling with the communication network makes better robustness of power system. But since the influences between the power and communication networks are asymmetric, the system parameters play an important role to determine the robustness of the whole system.

Assessing the Vulnerability of Megaprojects Using Complex Network Theory

This article examines the vulnerability of megaprojects using complex network theory. The megaproject is first abstracted as a weighted directed network, after which a novel vulnerability metric is designed to quantify megaproject vulnerability. The proposed approach is then applied to a megaproject, which demonstrates its effectiveness in assessing vulnerability and identifying critical projects. Several protection strategies are finally proposed to enhance megaproject management. Overall, this study proposes a quantitative method to assess megaproject vulnerability that can reduce vulnerability and assist in the development of proactive risk approaches to ensure successful megaproject completion.

Influencer identification in dynamical complex systems

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e. the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g. independent cascading models) or discontinuous phase transitions (e.g. threshold models). We conclude the review with a summary and an outlook.

Graph Theory Approach to the Vulnerability of Transportation Networks

Nowadays, transport is the basis for the functioning of national, continental, and global economies. Thus, many governments recognize it as a critical element in ensuring the daily existence of societies in their countries. Those responsible for the proper operation of the transport sector must have the right tools to model, analyze, and optimize its elements. One of the most critical problems is the need to prevent bottlenecks in transport networks. Thus, the main aim of the article was to define the parameters characterizing the transportation network vulnerability and select algorithms to support their search. The parameters proposed are based on characteristics related to domination in graph theory. The domination, edge-domination concepts, and related topics, such as bondage-connected and weighted bondage-connected numbers, were applied as the tools for searching and identifying the bottlenecks in transportation networks. Furthermore, the algorithms for finding the minimal dominating set and minimal (maximal) weighted dominating sets are proposed. This way, the exemplary academic transportation network was analyzed in two cases: stationary and dynamic. Some conclusions are presented. The main one is the fact that the methods given in this article are universal and applicable to both small and large-scale networks. Moreover, the approach can support the dynamic analysis of bottlenecks in transport networks.

Resilience Analysis of Critical Infrastructures: A Cognitive Approach Based on Granular Computing

A great impetus for the study of resilience in critical infrastructures (CIs) is found in the large number of initiatives and international research programmes from U.S., EU, and Asia. Politicians, decision makers, and citizens are now aware of the drastic consequences that can have the cascading effects of an adverse event in these large scale infrastructures. However, the study of resilience in CIs is challenging for several reasons, among which their large scale and interdependencies. We have to consider also that adverse events, e.g., attacks, natural hazards, or man-made disasters, suddenly occur and evolve rapidly, giving us little time to take decisions and react to them. Approximate reasoning and rapid decision making have to be considered requirements for resilience analysis of CIs. The main result presented in this paper relates to a systemic integration of granular computing (GrC) and resilience analysis for CIs. Each phase of our approach presents distinctive aspects but, overall, we argue the merit of this paper consists in the originality of the study, being this the first work that combines GrC and resilience analysis of CIs. This paper reports an illustrative example that shows how to apply our results, and a discussion on the necessary contextualizations and extensions of the GrC results to be better adapted for CIs resilience.

Generating symmetric graphs

Symmetry in graphs which describe the underlying topology of networked dynamical systems plays an essential role in the emergence of clusters of synchrony. Many real networked systems have a very large number of symmetries. Often one wants to test new results on large sets of random graphs that are representative of the real networks of interest. Unfortunately, existing graph generating algorithms will seldom produce graphs with any symmetry and much less ones with desired symmetry patterns. Here, we present an algorithm that is able to generate graphs with any desired symmetry pattern. The algorithm can be coupled with other graph generating algorithms to tune the final graph's properties of interest such as the degree distribution.

Intelligent Network DisRuption Analysis (INDRA): A targeted strategy for efficient interruption of hepatitis C transmissions

Hepatitis C virus (HCV) infection is a global public health problem. The implementation of public health interventions (PHI) to control HCV infection could effectively interrupt HCV transmission. PHI targeting high-risk populations, e.g., people who inject drugs (PWID), are most efficient but there is a lack of tools for prioritizing individuals within a high-risk community. Here, we present Intelligent Network DisRuption Analysis (INDRA), a targeted strategy for efficient interruption of hepatitis C transmissions.Using a large HCV transmission network among PWID in Indiana as an example, we compare effectiveness of random and targeted strategies in reducing the rate of HCV transmission in two settings: (1) long-established and (2) rapidly spreading infections (outbreak). Identification of high centrality for the network nodes co-infected with HIV or > 1 HCV subtype indicates that the network structure properly represents the underlying contacts among PWID relevant to the transmission of these infections. Changes in the network's global efficiency (GE) were used as a measure of the PHI effects. In setting 1, simulation experiments showed that a 50% GE reduction can be achieved by removing 11.2 times less nodes using targeted vs random strategies. A greater effect of targeted strategies on GE was consistently observed when networks were simulated: (1) with a varying degree of errors in node sampling and link assignment, and (2) at different levels of transmission reduction at affected nodes. In simulations considering a 10% removal of infected nodes, targeted strategies were ~2.8 times more effective than random in reducing incidence. Peer-education intervention (PEI) was modeled as a probabilistic distribution of actionable knowledge of safe injection practices from the affected node to adjacent nodes in the network. Addition of PEI to the models resulted in a 2-3 times greater reduction in incidence than from direct PHI alone. In setting 2, however, random direct PHI were ~3.2 times more effective in reducing incidence at the simulated conditions. Nevertheless, addition of PEI resulted in a ~1.7-fold greater efficiency of targeted PHI. In conclusion, targeted PHI facilitated by INDRA outperforms random strategies in decreasing circulation of long-established infections. Network-based PEI may amplify effects of PHI on incidence reduction in both settings.

Dynamically induced cascading failures in power grids

Reliable functioning of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. Although cascading failures often exhibit dynamical transients, the modeling of cascades has so far mainly focused on the analysis of sequences of steady states. In this article, we focus on electrical transmission networks and introduce a framework that takes into account both the event-based nature of cascades and the essentials of the network dynamics. We find that transients of the order of seconds in the flows of a power grid play a crucial role in the emergence of collective behaviors. We finally propose a forecasting method to identify critical lines and components in advance or during operation. Overall, our work highlights the relevance of dynamically induced failures on the synchronization dynamics of national power grids of different European countries and provides methods to predict and model cascading failures.

Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain

Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The proposed dynamic analysis approach calculated the adjacency matrices from ongoing electroencephalpgram (EEG) in a sliding time-window to form the FCGB sequences. The probability distribution of Shannon entropy was replaced by the connection sequence distribution to measure the uncertainty of FCGB constituting NE. Without averaging, we used time frequency transform of the NE of FCGB sequences to analyze the event-related changes in oscillatory activity in the single-trial traces during the complex cognitive process of driving. Finally, the results of a verification experiment showed that the NE of the FCGB sequences has a certain time-locked performance for different events related to driver fatigue in a prolonged driving task. The time errors between the extracted time of high-power NE and the recorded time of event occurrence were distributed within the range [−30 s, 30 s] and 90.1% of the time errors were distributed within the range [−10 s, 10 s]. The high correlation (r = 0.99997, p < 0.001) between the timing characteristics of the two types of signals indicates that the NE can reflect the actual dynamic interaction states of brain. Thus, the method may have potential implications for cognitive studies and for the detection of physiological states.

Restoration of services in disrupted infrastructure systems: A network science approach

Due to the ubiquitous nature of disruptive extreme events, functionality of the critical infrastructure systems (CIS) is constantly at risk. In case of a disruption, in order to minimize the negative impact to the society, service networks operating on the CIS should be restored as quickly as possible. In this paper, we introduce a novel network science inspired measure to quantify the criticality of components within a disrupted service network and develop a restoration heuristic (Cent-Restore) that prioritizes restoration efforts based on this measure. As an illustrative case study, we consider a road network blocked by debris in the aftermath of a natural disaster. The debris obstructs the flow of relief aid and search-and-rescue teams between critical facilities and disaster sites, debilitating the emergency service network. In this context, the problem is defined as finding a schedule to clear the roads with the limited resources. First, we develop a mixed-integer programming model for the problem. Then we validate the efficiency and accuracy of the Cent-Restore heuristic on randomly generated instances by comparing it to the model. Furthermore, we use Cent-Restore to recommend real-time restoration plans for disrupted road networks of Boston and Manhattan and analyze the performance of the plans over time through resilience curves. We compare Cent-Restore to the current restoration guidelines proposed by FEMA and other strategies that prioritize the restoration efforts based on different measures. As a result we confirm the importance of including specific post-disruption attributes of the networks to create effective restoration strategies. Moreover, we explore the relationship between a service network’s resilience and its topological and operational characteristics under different disruption scenarios. The methods and insights provided in this work can be extended to other disrupted large-scale critical infrastructure systems in which the ultimate goal is to enable the functions of the overlaying service networks.

Task-linked Diurnal Brain Network Reorganization in Older Adults: A Graph Theoretical Approach

Testing older adults in the morning generally improves behavioral performance relative to afternoon testing. Morning testing is also associated with brain activity similar to that of young adults. Here, we used graph theory to explore how time of day (TOD) affects the organization of brain networks in older adults across rest and task states. We used nodes from the automated anatomical labeling atlas to construct participant-specific correlation matrices of fMRI data obtained during 1-back tasks with interference and rest. We computed pairwise group differences for key graph metrics, including small-worldness and modularity. We found that older adults tested in the morning and young adults did not differ on any graph metric. Both of these groups differed from older adults tested in the afternoon during the tasks—but not rest. Specifically, the latter group had lower modularity and small-worldness (indices of more efficient network organization). Across all groups, higher modularity and small-worldness strongly correlated with reduced distractibility on an implicit priming task. Increasingly, TOD is seen as important for interpreting and reproducing neuroimaging results. Our study emphasizes how TOD affects brain network organization and executive control in older adults.

Recovery of infrastructure networks after localised attacks

The stability of infrastructure network is always a critical issue studied by researchers in different fields. A lot of works have been devoted to reveal the robustness of the infrastructure networks against random and malicious attacks. However, real attack scenarios such as earthquakes and typhoons are instead localised attacks which are investigated only recently. Unlike previous studies, we examine in this paper the resilience of infrastructure networks by focusing on the recovery process from localised attacks. We introduce various preferential repair strategies and found that they facilitate and improve network recovery compared to that of random repairs, especially when population size is uneven at different locations. Moreover, our strategic repair methods show similar effectiveness as the greedy repair. The validations are conducted on simulated networks, and on real networks with real disasters. Our method is meaningful in practice as it can largely enhance network resilience and contribute to network risk reduction.

Topological performance measures as surrogates for physical flow models for risk and vulnerability analysis for electric power systems

Critical infrastructure systems must be both robust and resilient in order to ensure the functioning of society. To improve the performance of such systems, we often use risk and vulnerability analysis to find and address system weaknesses. A critical component of such analyses is the ability to accurately determine the negative consequences of various types of failures in the system. Numerous mathematical and simulation models exist that can be used to this end. However, there are relatively few studies comparing the implications of using different modeling approaches in the context of comprehensive risk analysis of critical infrastructures. In this article, we suggest a classification of these models, which span from simple topologically-oriented models to advanced physical-flow-based models. Here, we focus on electric power systems and present a study aimed at understanding the tradeoffs between simplicity and fidelity in models used in the context of risk analysis. Specifically, the purpose of this article is to compare performance estimates achieved with a spectrum of approaches typically used for risk and vulnerability analysis of electric power systems and evaluate if more simplified topological measures can be combined using statistical methods to be used as a surrogate for physical flow models. The results of our work provide guidance as to appropriate models or combinations of models to use when analyzing large-scale critical infrastructure systems, where simulation times quickly become insurmountable when using more advanced models, severely limiting the extent of analyses that can be performed.

Impact of imperfect information on network attack

This paper explores the effectiveness of network attack when the attacker has imperfect information about the network. For Erdős-Rényi networks, we observe that dynamical importance and betweenness centrality-based attacks are surprisingly robust to the presence of a moderate amount of imperfect information and are more effective compared with simpler degree-based attacks even at moderate levels of network information error. In contrast, for scale-free networks the effectiveness of attack is much less degraded by a moderate level of information error. Furthermore, in the Erdős-Rényi case the effectiveness of network attack is much more degraded by missing links as compared with the same number of false links.

Distance metric learning for complex networks: towards size-independent comparison of network structures

Real networks show nontrivial topological properties such as community structure and long-tail degree distribution. Moreover, many network analysis applications are based on topological comparison of complex networks. Classification and clustering of networks, model selection, and anomaly detection are just some applications of network comparison. In these applications, an effective similarity metric is needed which, given two complex networks of possibly different sizes, evaluates the amount of similarity between the structural features of the two networks. Traditional graph comparison approaches, such as isomorphism-based methods, are not only too time consuming but also inappropriate to compare networks with different sizes. In this paper, we propose an intelligent method based on the genetic algorithms for integrating, selecting, and weighting the network features in order to develop an effective similarity measure for complex networks. The proposed similarity metric outperforms state of the art methods with respect to different evaluation criteria.

Structure and function of complex brain networks

An increasing number of theoretical and empirical studies approach the function of the human brain from a network perspective. The analysis of brain networks is made feasible by the development of new imaging acquisition methods as well as new tools from graph theory and dynamical systems. This review surveys some of these methodological advances and summarizes recent findings on the architecture of structural and functional brain networks. Studies of the structural connectome reveal several modules or network communities that are interlinked by hub regions mediating communication processes between modules. Recent network analyses have shown that network hubs form a densely linked collective called a "rich club," centrally positioned for attracting and dispersing signal traffic. In parallel, recordings of resting and task-evoked neural activity have revealed distinct resting-state networks that contribute to functions in distinct cognitive domains. Network methods are increasingly applied in a clinical context, and their promise for elucidating neural substrates of brain and mental disorders is discussed.

Multiple resource demands and viability in multiplex networks

Many complex systems demand manifold resources to be supplied from distinct channels to function properly, e.g., water, gas, and electricity for a city. Here, we study a model for viability of such systems demanding more than one type of vital resource be produced and distributed by resource nodes in multiplex networks. We found a rich variety of behaviors such as discontinuity, bistability, and hysteresis in the fraction of viable nodes with respect to the density of networks and the fraction of resource nodes. Our result suggests that viability in multiplex networks is not only exposed to the risk of abrupt collapse but also suffers excessive complication in recovery.

Error and attack vulnerability of temporal networks

The study of real-world communication systems via complex network models has greatly expanded our understanding on how information flows, even in completely decentralized architectures such as mobile wireless networks. Nonetheless, static network models cannot capture the time-varying aspects and, therefore, various temporal metrics have been introduced. In this paper, we investigate the robustness of time-varying networks under various failures and intelligent attacks. We adopt a methodology to evaluate the impact of such events on the network connectivity by employing temporal metrics in order to select and remove nodes based on how critical they are considered for the network. We also define the temporal robustness range, a new metric that quantifies the disruption caused by an attack strategy to a given temporal network. Our results show that in real-world networks, where some nodes are more dominant than others, temporal connectivity is significantly more affected by intelligent attacks than by random failures. Moreover, different intelligent attack strategies have a similar effect on the robustness: even small subsets of highly connected nodes act as a bottleneck in the temporal information flow, becoming critical weak points of the entire system. Additionally, the same nodes are the most important across a range of different importance metrics, expressing the correlation between highly connected nodes and those that trigger most of the changes in the optimal information spreading. Contrarily, we show that in randomly generated networks, where all the nodes have similar properties, random errors and intelligent attacks exhibit similar behavior. These conclusions may help us in design of more robust systems and fault-tolerant network architectures.

The reconstruction of transcriptional networks reveals critical genes with implications for clinical outcome of multiple myeloma

PURPOSE

The combined use of microarray technologies and bioinformatics analysis has improved our understanding of biological complexity of multiple myeloma (MM). In contrast, the application of the same technology in the attempt to predict clinical outcome has been less successful with the identification of heterogeneous molecular signatures. Herein, we have reconstructed gene regulatory networks in a panel of 1,883 samples from MM patients derived from publicly available gene expression sets, to allow the identification of robust and reproducible signatures associated with poor prognosis across independent data sets.

EXPERIMENTAL DESIGN

Gene regulatory networks were reconstructed by using Algorithm for the Reconstruction of Accurate Cellular Networks (ARACNe) and microarray data from seven MM data sets. Critical analysis of network components was applied to identify genes playing an essential role in transcriptional networks, which are conserved between data sets.

RESULTS

Network critical analysis revealed that (i) CCND1 and CCND2 were the most critical genes; (ii) CCND2, AIF1, and BLNK had the largest number of connections shared among the data sets; (iii) robust gene signatures with prognostic power were derived from the most critical transcripts and from shared primary neighbors of the most connected nodes. Specifically, a critical-gene model, comprising FAM53B, KIF21B, WHSC1, and TMPO, and a neighbor-gene model, comprising BLNK shared neighbors CSGALNACT1 and SLC7A7, predicted survival in all data sets with follow-up information.

CONCLUSIONS

The reconstruction of gene regulatory networks in a large panel of MM tumors defined robust and reproducible signatures with prognostic importance, and may lead to identify novel molecular mechanisms central to MM biology.

Node vulnerability under finite perturbations in complex networks

A measure to quantify vulnerability under perturbations (attacks, failures, large fluctuations) in ensembles (networks) of coupled dynamical systems is proposed. Rather than addressing the issue of how the network properties change upon removal of elements of the graph (the strategy followed by most of the existing methods for studying the vulnerability of a network based on its topology), here a dynamical definition of vulnerability is introduced, referring to the robustness of a collective dynamical state to perturbing events occurring over a fixed topology. In particular, we study how the collective (synchronized) dynamics of a network of chaotic units is disrupted under the action of a finite size perturbation on one of its nodes. Illustrative examples are provided for three systems of identical chaotic oscillators coupled according to three distinct well-known network topologies. A quantitative comparison between the obtained vulnerability rankings and the classical connectivity/centrality rankings is made that yields conclusive results. Possible applications of the proposed strategy and conclusions are also discussed.

Robustness of trans-European gas networks

Here, we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on intercountry flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual purpose. On one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a nonoperational pipeline causes only a minimal impact on network capacity, implying that the network is error tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.

Power grid vulnerability: a complex network approach

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.

Network pharmacology: the next paradigm in drug discovery

The dominant paradigm in drug discovery is the concept of designing maximally selective ligands to act on individual drug targets. However, many effective drugs act via modulation of multiple proteins rather than single targets. Advances in systems biology are revealing a phenotypic robustness and a network structure that strongly suggests that exquisitely selective compounds, compared with multitarget drugs, may exhibit lower than desired clinical efficacy. This new appreciation of the role of polypharmacology has significant implications for tackling the two major sources of attrition in drug development--efficacy and toxicity. Integrating network biology and polypharmacology holds the promise of expanding the current opportunity space for druggable targets. However, the rational design of polypharmacology faces considerable challenges in the need for new methods to validate target combinations and optimize multiple structure-activity relationships while maintaining drug-like properties. Advances in these areas are creating the foundation of the next paradigm in drug discovery: network pharmacology.

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.

Empirical analysis of the ship-transport network of China

Structural properties of the ship-transport network of China (STNC) are studied in the light of recent investigations of complex networks. STNC is composed of a set of routes and ports located along the sea or river. Network properties including the degree distribution, degree correlations, clustering, shortest path length, centrality, and betweenness are studied in different definitions of network topology. It is found that geographical constraint plays an important role in the network topology of STNC. We also study the traffic flow of STNC based on the weighted network representation, and demonstrate the weight distribution can be described by power-law or exponential function depending on the assumed definition of network topology. Other features related to STNC are also investigated.

Random walks along the streets and canals in compact cities: spectral analysis, dynamical modularity, information, and statistical mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of Genius loci. Global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem.

Structural properties of planar graphs of urban street patterns

Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological, and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are turned into spatial valued graphs. In such graphs, the nodes are embedded in the two-dimensional plane and represent street intersections, the edges represent streets, and the edge values are equal to the street lengths. We evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four, and five edges), and the global properties by measuring global efficiency and cost. We also consider, as extreme cases, minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The measures found in the real and the artificial networks are then compared. Surprisingly, cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties. The correlation between a priori known classes and statistical properties is illustrated in a plot of relative efficiency vs cost.

Centrality in networks of urban streets

Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structure, nicely capturing the skeleton of most central routes and subareas that so much impacts on spatial cognition and on collective dynamical behaviors. Statistically, closeness, straightness and betweenness turn out to follow similar functional distribution in all cases, despite the extreme diversity of the considered cities. Conversely, information is found to be exponential in planned cities and to follow a power-law scaling in self-organized cities. Hierarchical clustering analysis, based either on the Gini coefficients of the centrality distributions, or on the correlation between different centrality measures, is able to characterize classes of cities.