Random Node Failures Research Articles

Fragility Induced by Interdependency of Complex Networks and Their Higher-Order Networks

The higher-order structure of networks is a hot research topic in complex networks. It has received much attention because it is closely related to the functionality of networks, such as network transportation and propagation. For instance, recent studies have revealed that studying higher-order networks can explore hub structures in transportation networks and information dissemination units in neuronal networks. Therefore, the destruction of the connectivity of higher-order networks will cause significant damage to network functionalities. Meanwhile, previous works pointed out that the function of a complex network depends on the giant component of the original(low-order) network. Therefore, the network functionality will be influenced by both the low-order and its corresponding higher-order network. To study this issue, we build a network model of the interdependence of low-order and higher-order networks (we call it ILH). When some low-order network nodes fail, the low-order network's giant component shrinks, leading to changes in the structure of the higher-order network, which further affects the low-order network. This process occurs iteratively; the propagation of the failure can lead to an eventual network crash. We conducted experiments on different networks based on the percolation theory, and our network percolation results demonstrated a first-order phase transition feature. In particular, we found that an ILH is more fragile than the low-order network alone, and an ILH is more likely to be corrupted in the event of a random node failure.

Resilience of supply-chain systems under perturbations: A network approach.

Supply-chain systems (SCSs) are an indispensable part of our daily infrastructures. Note that a small perturbation in a SCS can be amplified, eliciting cascading failures. It is of significant value to ensure a high resilience of SCSs. However, due to the complexity of SCSs, it is quite challenging to study their resilience under conditions of perturbations. In view of this, this paper presents a complex network perspective toward the resilience of SCSs. To achieve this goal, a complex SCS is modeled as a multilayer supply-chain network (SCN) with physical organizations being modeled as nodes and interactions among them as edges. A modeled SCN contains three types of nodes, i.e., suppliers, manufacturers, and retailers. An algorithm is proposed to construct a multilayer SCN. For each layer of a multilayer SCN, two kinds of networks, i.e., networks with Poisson degree distributions and networks with power-law degree distributions, are considered. For a given multilayer SCN, a ripple-effect network model is proposed to analyze its resilience under perturbations. Regarding the perturbations, two scenarios, i.e., random node failures and target node failures, are adopted in this research. In order to validate the effectiveness of the proposed network perspective, simulations on computer-generated SCNs are carried out. Interestingly, it is found that the resilience of SCNs under both random and target perturbations presents a discontinuous phase-change phenomenon, which indicates that SCNs are quite fragile under perturbations. It is further noticed that SCNs with power-law degree distributions are relatively more robust than SCNs with Poisson degree distributions. Although SCNs are found to be fragile, it has been discovered that denser interactions between different system organizations can enhance the network's resilience.

Research on the Robustness of the Chinese Input-Output Network Based on Relative Entropy Theory.

The input–output (IO) network is the quantitative description of an IO-based economy in which nodes represent industries and edges connecting nodes represent the economic connection between industries. Robustness refers to the ability of tolerating perturbations that might affect the system’s functional body. There is both practical and theoretical significance to explore the robustness of the IO network for economic development. In this paper, we probe the robustness of the Chinese IO network based on the relative entropy of the probability distribution of network parameters (node degree, strongest path betweenness, downstream closeness and upstream closeness) under random node or edge failure and intentional node or edge attack. It is found that the Chinese IO network shows relatively weak robustness when it is under intentional attack, but relatively strong robustness when it is under random failure. Our experiment also verifies the applicability and effectiveness of the relative entropy model in measuring the robustness of the IO network.

The robustness of the photosynthetic system I energy transfer complex network to targeted node attack and random node failure

Abstract In this article, we implement and compare 10 node removal (attack) strategies from the literature over the photosystem I (PSI) complex network of the common pea plant (Pisum sativum), representing the FRET energy transfer among its nodes/chromophores. We measure the network robustness (functioning) with four indicators. The node attack strategies and the network robustness indicators consider both the binary-topological and the weighted structure of the network. First, we find that the well-known node betweenness centrality attack, which has proven highly effective in dismantling most real-world networks’ topological connectivity, is ineffective over the PSI network. Second, the degeneracy of the node properties caused by the PSI’s higher network connectivity level induces a random-like node removal even when nodes are removed according to a specific node centrality measure. This phenomenon triggers a very low decrease of the PSI network functioning even when subjected to node attack. Such an outcome would indicate that the node attack strategies based on classic node properties, such as the degree or the betweenness centrality, may show low efficacy in dismantling real-world networks with very high connectivity levels. Last, the PSI network can be built by tuning a cut-off distance (CD) that defines the viable energy transfers among nodes/chromophores and progressively discards the lower energy transfer links among distant nodes/chromophores. This represents a ‘weight thresholding’ procedure allowing us to investigate the efficacy of the node attack strategies when links of lower weight are progressively pruned from the PSI network. We find that the best node attack strategies change by decreasing the CD, showing that the weight thresholding procedure affects the network response to node removal. This last outcome outlines the importance of investigating the stability of the system response for real-world weighted complex networks subjected to the weight thresholding procedure.

Dynamic hypergraphs of renewal processes in mobile networks.

The characteristics of random geometric hypergraphs are studied as mathematical models of scalable wireless computer networks. An efficient algorithm for finding cliques in geometric graphs, constructing hypergraphs from geometric configurations has been developed. The types of hyper-edges in hypergraphs generated by a scalable configuration have been identified. The influence of random failures of nodes of computer networks and their restorations on the dynamics of hypergraphs of networks is considered. The analysis of the dynamics of the number of active nodes depending on the type of probability distributions of uptime and recovery time is carried out. The dependences of the mathematical expectation of the number of hyper-edges of certain types in the geometric hypergraph of a wireless computer network on the network operation time, on the radii of zones of reliable reception / transmission of a signal, on the ratio of the parameters of local recovery processes are obtained. The presentation of the results is accompanied by charts.

A study of the stability of information and telecommunication networks under conditions of stochastic percolation of nodes

In-depth studies of the topological properties of information and telecommunication networks contribute to the understanding of their functional capabilities, including stability. The study of the stability of complex networks to failures in operation when their components fail is based on modeling by sequentially removing nodes or edges of the network (percolation). The paper presents a comparative analysis of sequential and stochastic variants of percolation of network nodes and statistical estimates of the complex two-criterion network stability coefficient. During the study, methods for calculating the average path length based on graph theory were used. In the statistical analysis of the network stability, we applied the analysis of variance and pairwise comparisons according to the Tukey criterion, based on the provisions of the theory of mathematical statistics. The simulation is performed using the Barabashi–Albert and Erdős–Rényi random graph models. The difference between the method of stochastic percolation and sequential percolation is shown. The performed statistical analysis proved the influence of the factor changing the structure of networks on their stability due to stochastic percolation. The dynamics of network stability reduction under stochastic percolation for different types of networks is shown. It is revealed that in some cases, for example, in networks with high density, the stochastic percolation method is the most preferable one. The study shows the possible options for assessing the stability of networks without a priori knowledge about the type of connections between nodes and with a priori knowledge about the type of connections between nodes. In the former case, knowing the number of network nodes, one can calculate the limit values of stability, in the same way as if the nodes were deleted accidentally. The latter option can be used to calculate the stability of networks that are subject to random node failures, for example, when diagnosing technical systems.

Robustness evaluation for real traffic network from complex network perspective

Robustness is a critical characteristic of ubiquitous real networked systems which are often very vulnerable to the random failures or targeted attacks. In this work, we aim to evaluate the robustness of a traffic network which is constructed from real trajectory data. First, we divide a city into grids which are considered as nodes and a link is established if there is at least one taxi dispatch order from one grid to another. Second, we propose two categories of attack strategies: node attacks (e.g. random node failure, and degree, in-degree, out-degree, closeness, clustering coefficient, PageRank-based targeted attacks) and link attacks (e.g. random link failure and link weight, link degree, link betweenness-based targeted attacks). Third, we suppose all elements (i.e. node or link) are simultaneously or iteratively removed, and evaluate the network robustness by employing the relative size of the giant components, average clustering coefficient and average shortest path length. The results show that the degree-based targeted attacks are the most destructive among all attacks, and no matter node or link, the betweenness-based attack is the most effective method to be beneficial to the target index. Moreover, most methods with recalculations take priority over the ones without recalculations.

The Conditional Strong Matching Preclusion of Augmented Cubes

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties.

Percolation thresholds for robust network connectivity

Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation (resp., deletion) probability or an edge activation (resp., removal) probability above (resp., below) which there exists a giant connected component (GCC), a connected component comprising of a number of occupied nodes and active edges whose size is proportional to the size of the network itself. Any pair of occupied nodes in the GCC is connected via at least one path comprised of active edges and occupied nodes. The mere existence of the GCC itself does not guarantee that the long-range connectivity would be robust, e.g. to random link or node failures due to network dynamics. In this paper, we explore new percolation thresholds that guarantee not only spanning network connectivity, but also robustness. We define and analyze four measures of robust network connectivity, explore their interrelationships, and numerically evaluate the respective robust percolation thresholds for the 2D square lattice.

Breakup of Directed Multipartite Networks

A complex network in reality often consists of profuse components, which might suffer from unpredictable perturbations. Because the components of a network could be interdependent, therefore the failures of a few components may trigger catastrophes to the entire network. It is thus pivotal to exploit the robustness of complex networks. Existing studies on network robustness mainly deal with interdependent or multilayer networks; little work is done to investigate the robustness of multipartite networks, which are an indispensable part of complex networks. Here, we plumb the robustness of directed multipartite networks. To be specific, we exploit the robustness of bi-directed and unidirectional multipartite networks in face of random node failures. We, respectively, establish cascading and non-cascading models based on the largest connected component concept for depicting the dynamical processes on bi-directed and unidirectional multipartite networks subject to perturbations. Based on our developed models, we, respectively, derive the corresponding percolation theories for mathematically computing the robustness of directed multipartite networks subject to random node failures. We unravel the first-order and second-order phase transition phenomena on the robustness of directed multipartite networks. The correctness of our developed theories has been verified through experiments on computer-generated as well as real-world multipartite networks.

Continuous Phase Transition of k-Partite Networks

Our daily lives rely on all kinds of complex networks. However, complex networks in reality often suffer from random failures and/or attacks that can cause failures to their nodes/edges. A network can totally lose its functionalities due to nodes/edges failures. It is, therefore, of great significance to assess the robustness of complex networks confronted with failures. The network robustness analysis is helpful for assuring the reliability of complex networks. In our previous work, we had experimentally investigated the robustness of a special type of networks called k-partite networks. Simulation results have discovered that k-partite networks are robust to random node failures. In this work, we aim to investigate the underlying mathematical principle for the robustness property of k-partite networks. To do so, we have developed the mathematical theory to calculate the robustness of k-partite networks to random node failures. The developed theory mathematically uncovers the continuous phase transition of the robustness of k-partite networks under random node failures. In order to check if the developed theory is correct, we experimentally test the robustness of computer generated k-partite networks. The experimental results and the one calculated using the proposed theory comply with each other, which proves that the proposed theory is correct.

Percolation Theories for Multipartite Networked Systems under Random Failures

Real-world complex systems inevitably suffer from perturbations. When some system components break down and trigger cascading failures on a system, the system will be out of control. In order to assess the tolerance of complex systems to perturbations, an effective way is to model a system as a network composed of nodes and edges and then carry out network robustness analysis. Percolation theories have proven as one of the most effective ways for assessing the robustness of complex systems. However, existing percolation theories are mainly for multilayer or interdependent networked systems, while little attention is paid to complex systems that are modeled as multipartite networks. This paper fills this void by establishing the percolation theories for multipartite networked systems under random failures. To achieve this goal, this paper first establishes two network models to describe how cascading failures propagate on multipartite networks subject to random node failures. Afterward, this paper adopts the largest connected component concept to quantify the networks’ robustness. Finally, this paper develops the corresponding percolation theories based on the developed network models. Simulations on computer-generated multipartite networks demonstrate that the proposed percolation theories coincide quite well with the simulations.

Resilient greedy routing on GPS-free surface sensor networks

We design a greedy routing scheme specifically for GPS-free large-scale wireless sensor networks deployed on surfaces of complex-connected three-dimensional settings. Compared with other greedy embedding–based surface network routing scheme, the proposed one is cut free such that no pair of nodes suffers a long detour to reach each other. The routing scheme is designed to be resilient to node or link failures especially under random node or link failure model where each node in a network has an equal and independent probability of failure during some time interval. The proposed algorithm is fully distributed and scalable to both the size and the topological complexity of a network. Each sensor node requires only limited and constant storage. Simulation results show the proposed routing scheme with a higher successful delivery ratio, a lower average stretch factor, and a lower normalized communication cost compared with other resilient routing methods.

A Study on PHF-Tau Network Effected by Apolipoprotein E4.

Apolipoprotein E 4 Allele (APOE 4) is an important factors in Mild cognitive impairment (MCI) and Alzheimer's disease(AD). It plays a primary role in abnormal modification of aggregated Tau protein-paired helical filaments Tau (PHF-Tau). In this study, 143 subjects with PHF-Tau PET were divided into 2 groups (APOE 4 carriers and noncarriers). The measurements of the PHF-Tau network properties and resilient were calculated for 2 group networks respectively. APOE 4 carriers group showed significant differences in all the network properties in the results. We also found significant differences of betweenness centrality in some brain regions for APOE 4 carriers. Moreover, the APOE 4 carriers showed less resilient to targeted or random node failure. Our results indicated that the effects of APOE 4 may lead to abnormalities of PHF-Tau protein network. These findings may be particularly helpful in uncovering the pathophysiology underlying the cognitive dysfunction in MCI patients.

Characterising the robustness of coupled power-law networks

Many networks exhibit a power-law configuration, where the number of connections each node has follows a power-law distribution, including the Internet, terrorist cells, species relationships and infrastructure. Given the prevalence of power-law networks, studying the effects of disruptions on their performance is of interest. Previous work has investigated the influence of network topology on the effects of random node failures for independent networks. Many networks depend on others to function and thus, exploring the influence of network topology on the effects of failures in interdependent networks is of interest. The present paper extends the previous work to coupled power-law network systems. For a set of randomly generated coupled systems, each containing two networks, we investigate the significant topological factors for different dependency types. Failures in the coupled networks are simulated and the effects on the system performance are analysed by performing a beta regression. The results are consistent across the dependency types, with the most influential topological factors being mean nodal degree and factors relating to the dependency type. The results are also compared with those of the independent networks and their potential relevance to the design of interdependent networks is indicated, for example, their use within an infrastructure setting.

Structural alterations of the brain preceded functional alterations in major depressive disorder patients: Evidence from multimodal connectivity

BackgroundRecent studies showed that major depressive disorder (MDD) has been involved in abnormal functional and structural connections in specific brain regions. However, comprehensive researches on MDD-related alterations in the topological organization of brain functional and structural networks are still limited. MethodsFunctional network (FN) was constructed from resting-state functional MRI temporal series correlations and structural network (SN) was established by Diffusion tensor imaging (DTI) data in 58 MDD patients and 71 healthy controls (HC). The measurements of the network properties were calculated for two networks respectively. Correlations were conducted between altered network parameters and Hamilton depression scale (HAMD) score. Additionally, network resilient analysis were conducted on FN and SN. ResultsThe losses of small-worldness charateristics and the decline of nodal efficiency across FN and SN were found in MDD patients. Based on network-based statistic (NBS) approach, the decreased connections in MDD patients were mainly found in the superior occipital gyrus, superior temporal gyrus for FN and SN, while the increased connections were distributed in putamen, superior frontal gyrus only for SN. Compared with the FN, the SN showed less resilient to targeted or random node failure. Besides, altered edges in NBS and regions with decreased nodal efficiency were negatively associated with HAMD score in MDD patients. LimitationsThe samples size is small and most of the MDD patients take different antidepressant medications. ConclusionsAlterations of SN in the brain of MDD patients preceded that of FN to some extent, and reorganization of the brain network was a mechanism which compensated for functional and structural alterations during disease progression.

Robustness of multipartite networks in face of random node failure

Abstract Complex networks are prevalent in our lives. A complex network usually is composed of many components. Because the components of a network may suffer from random failures or intentional attacks, it is therefore important to study the robustness of networks in face of perturbations. Because real-world complex networks are practically interdependent, therefore many efforts have been made to investigate the robustness of interdependent or multilayer networks. Existing studies indicate that the robustness of multilayer networks displays first order phase transition, while the robustness of single layer networks only displays second order phase transition. Note that a simple form of a multilayer network is a multipartite network. Intuitively, the robustness of multipartite networks will also possess first order phase transition. In this paper we study the robustness of multipartite networks in face of random node failures. Extensive experiments have been carried out to test the robustness of multipartite networks whose degree distributions follow Poisson distribution. Interestingly, we have found that the robustness of multipartite networks displays second-order-like phase transition which is against the intuitive conclusion.

A Probabilistic Theory Based Method for Robustness Assessment of Bipartite Networks

Complex networks play a significant role in our daily lives. Due to the fact that complex networks, in reality, could suffer from manifold perturbations and network components could break down, it is, therefore, pivotal to investigate the robustness of complex networks in the face of perturbations. In the literature, enormous endeavors have been made to study network robustness. However, existing studies mainly deal with the interdependent networks, while little attention is paid to study the robustness of bipartite networks. Many networks, such as economical networks and biological networks, can be modeled as bipartite networks. It is therefore important to study the robustness of bipartite networks. Because the structures of bipartite networks differ from that of networks in common sense, existing robustness analysis methods cannot be applied to bipartite networks. With regard to this, this paper proposes a generic method based on the probabilistic theory to assess the robustness of bipartite networks under random node failures. The proposed method mathematically indicates that bipartite networks are robust to random perturbations. The experiments on random bipartite Erdos–Renyi and scale-free networks demonstrate that the theoretical results yielded by the proposed method coincide quite well with the simulation results. This paper also compares the proposed method against the well-studied method. The experiments indicate that the proposed method outperforms the comparison method.

Dynamic Analysis for the Average Shortest Path Length of Mobile Ad Hoc Networks Under Random Failure Scenarios

In general, the mobile ad hoc networks (MANETs) are built on the basis of the random distribution of the nodes, while the nodes of real networks usually have the characteristics of location preference choice. The evolving network model based on local-area choice is proposed for MANET based on the complex network theory. The proposed model of the topology not only considers the scale-free nature of the network and the actual mobility of MANET but also considers the consumption of the node energy. Random failures often occur in MANET. Most of the existing research focuses on the changes in network topology caused by random node failures. In order to describe the impact of random edge failures on the topology of MANET, we focus on the average shortest path length (ASPL) which is an important feature of the network topology and propose the formula for calculating the ASPL of the MANET after the random edge failure. The experimental simulation analyzes the change of the ASPL of MANET in the random failure scenario (after random edge deletion). By comparing with the actual scene results, the proposed estimation formula which describes this change more accurately is proved. The formula proposed in this paper provides a general framework for studying the shortest path of MANET.

A dynamic evolution model of balanced energy consumption scale-free fault-tolerant topology based on fitness function for wireless sensor networks

The network life can be prolonged to some extent by the scale-free topology which has strong fault-tolerance for the random failure of nodes. However, the unevenness of the scale-free topological structure can result in the imbalance of consumption of network. In order to resolve the problem, a dynamic evolution model of consumption of balanced energy with scale-free fault-tolerant topology based on fitness function for wireless sensor networks is proposed. First, the effect of nodal energy and the distance between the nodes on the network life is analysed as per the energy consumption model. Thereafter, the ratio between the residual energy of the node and the distance between nodes is used as the fitness function along with the dynamic behaviour of link and variations in network topology. Thus, a fault-tolerant topology model with scale-free properties is obtained. The simulation results indicate that the proposed model can not only balance the energy consumption of the nodes and the network by prolonging the life of network, but can enhance the fault tolerance and the invasion ability of the network by comparing with Barabasi-Albert model (BA), energy aware evolution model (EAEM) and fault-tolerant topological model with energy consumption and load (FTEL).