Power-law Degree Distribution Research Articles

The comparison of Chinese and Australian aviation networks under the most important node attacks

Air traffic plays an important role in the economy and daily life both in developing and developed countries, The shutdown of the crucial airport will lead to large financial losses. In this study, the data have been collected from Openflight.org with information of flights and routes. Then the characteristics of the Chinese aviation network and Australian aviation network have been computed. The results indicate that the Chinese aviation network and Australian aviation network are both scale-free networks of power-law degree distribution with long-tail attributes. Then, the centrality analysis of the top 10 airports in the Chinese aviation network and Australian aviation network have been assessed, such as betweenness centrality analysis and closeness centrality analysis. Lastly, the study looks into how the characteristics of the Chinese and American aviation networks have changed as a result of node attacks and offers helpful advice for both the Chinese and Australian aviation networks after the most important node attacks.

Mitigation of adversarial attacks on voter model dynamics by network heterogeneity

Voter model dynamics in complex networks are vulnerable to adversarial attacks. In particular, the voting outcome can be inverted by adding extremely small perturbations that are strategically generated in social networks, even when one opinion is dominant over the other. However, the mitigation of adversarial attacks on the voter model dynamics in complex networks has not been thoroughly investigated. Thus, we examined network structures that could mitigate adversarial attacks using model networks and real-world networks, considering that the network structure affects the voter model dynamics. Numerical simulations demonstrated that the heterogeneity of node degrees in the networks (degree heterogeneity) significantly mitigates adversarial attacks. In particular, for complex networks with a power-law degree distribution , the mitigation effect is significant for . However, the mitigation effect of the degree heterogeneity was relatively weak for large and dense networks. The degree correlation and clustering in the networks exhibited almost no mitigation effect. The results enhance our understanding of how opinion dynamics and collective decision-making are distorted in social networks and may be useful for considering defense strategies against adversarial attacks.

Integrated analysis of topoisomerase I inhibitors from flavonoids of Scutellaria baicalensis Georgi using bioaffinity ultrafiltration UPLC-TripleTOF MS/MS, molecular docking and target-based multiple complex networks

Scutellaria baicalensis Georgi (SBG) has been widely used as medical plant in East Asia with remarkable anti-cancer activity. However, the underlying mechanisms are still confused. In this study, an integrated analysis was conducted to screen topoisomerase I (topo I) inhibitors from flavonoids of SBG and investigate the anti-cancer mechanisms, containing bioaffinity ultrafiltration UPLC-ESI-TripleTOF-MS/MS, molecular docking, and multiple complex networks. The SBG extract exhibited notable cytotoxic activity on Hela cells. Five flavonoids were identified as potential topo I inhibitors, including skullcapflavone II, wogonin, chrysin, oroxylin A, and tenaxin I. Their ESI-MS/MS spectra showed that RDA reaction and neutral molecule loss were the main fragment patterns. Docking results demonstrated that π–π interaction and the formation of hydrogen bond contributed most to their binding with topo I. The selected compounds, related target proteins and pathways were integrated into target-based multiple complex networks, which consisted of three subnetworks. Statistical and topological analysis of these networks revealed a series of characteristics, including scale-free property with power-law degree distribution, Poisson degree distribution, and small-world property. Chrysin, wogonin, and oroxylin A exhibited as main active components with much higher degree values. Chemical carcinogenesis-receptor activation (hsa05207) was considered as critical pathway due to remarkable centrality indexes. Additionally, potential synergistic effect of wogonin and chrysin was observed on the conversion of supercoiled DNA to relaxed forms. These results improved current understanding of flavonoid-rich plants on the treatment of cancer. Moreover, the multi-disciplinary approach provided a new strategy for the research of natural products from medical plants.

Double power-law distribution in spatial network induced by cost constraints

We investigate the scaling laws of the degree distribution in an evolving spatial network where the long-range links of a node are subject to a cost constraint. The constraint can cause a discontinuous reduction in the length of the links to be attached to the node once the node reaches some critical degree k c . We show that this effect can result in an abrupt change in the attachment probability and consequently induces a double power-law degree distribution. We derive the distribution analytically for the homogeneous constraint and demonstrate a consistent result for the heterogeneous one. Our model finds a robust connection between the double power law and the spatial constraint and offers a plausible explanation of the common occurrence of the distribution in airline networks.

Robustness analysis of electricity networks against failure or attack: The case of the Australian National Electricity Market (NEM)

This study explores network science algorithms for the robustness analysis of electricity networks. We first investigate the characteristics of key network models including random graphs, small-world, and scale-free networks. Then, various measures are explored for the robustness of such networks against failure or attack, utilizing topological features and percolation theory. Both weighted and unweighted scenarios are studied, with network voltage considered as the edge weight. For a case study, we investigate the network characteristics as well as the robustness of the Australian National Electricity Market (NEM) network on the basis of these models and theories.The NEM is the world's longest interconnected power system, with an end-to-end distance of over 5000 km between the state of Queensland in the north and the state of South Australia. Our data contains 2375 transmission lines and 1538 nodes as generators or large demand customers. Our study shows that the NEM as an unweighted network is a small-world network (with exponential degree distribution). However, as a weighted network (considering the voltage capacity of nodes), it has a scale-free topology (following a power-law degree distribution). Robustness analysis revealed that the NEM presents relatively stronger robustness when facing random errors than when facing intentional attacks to nodes with a high degree centrality. It also revealed the sensitivity of the scale-free network to deliberate attacks directed toward important “hubs” (interconnected nodes).

A Generalized Configuration Model With Triadic Closure

In this paper we present a generalized configuration model with random triadic closure (GCTC). This model possesses five fundamental properties: large clustering coefficient, power law degree distribution, short path length, non-zero Pearson degree correlation, and existence of community structures. We analytically derive the Pearson degree correlation coefficient and the clustering coefficient of the proposed model. We select a few datasets of real-world networks. By simulation, we show that the GCTC model matches very well with the datasets in terms of Pearson degree correlations and clustering coefficients. We also test three well-known community detection algorithms on our model, the datasets and other three prevalent benchmark models. We show that the GCTC model performs equally well as the other three benchmark models. Finally, we perform influence diffusion on the GCTC model using the independent cascade model and the linear threshold model. We show that the influence spreads of the GCTC model are much closer to those of the datasets than the other benchmark models. This suggests that the GCTC model is a suitable tool to study network science problems where degree correlation or clustering plays an important role.

GRASP: Scalable Graph Alignment by Spectral Corresponding Functions

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this article, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

DRONE: An Efficient Distributed Subgraph-Centric Framework for Processing Large-Scale Power-law Graphs

Nowadays, the ever-increasing volume of graph-structured data such as social networks, graph databases and knowledge graphs requires to be processed efficiently and scalably. These natural graphs commonly found in the real world have highly skewed power-law degree distribution and are called power-law graphs. The subgraph-centric programming model is a promising approach applied in many state-of-the-art distributed graph computing frameworks. However, the performance of subgraph-centric frameworks is limited when processing large-scale power-law graphs. When deployed to the subgraph-centric framework, existing graph partitioning algorithms are not suitable for power-law graphs. In this paper, we present a novel distributed graph computing framework, DRONE (Distributed gRaph cOmputiNg Engine), which leverages the subgraph-centric model and the vertex-cut graph partitioning strategy. DRONE also supports the fault tolerance mechanism to accommodate the increasing scale of machines with negligible overhead (6.48% on average). We further study the execution workflow of DRONE and propose an efficient and balanced graph partition algorithm (EBV) for DRONE. Experiments show that DRONE reduces the running time on real-world graphs by 25.6%, on average, compared to the state-of-the-art distributed graph computing frameworks. In addition, the EBV graph partition algorithm reduces the replication factor by at least 21.8% than other self-based partition algorithms. Our results indicate that DRONE has excellent potential in processing large-scale power-law graphs.

The impact of default on the evolving dynamic networks of debtor-creditor relationships

The aim of this study was to study the underlying structural characteristics of networks formed by debtor-creditor relationships. According to attributes of P2P lending, this paper model the networks of debtor-creditor relationships as an evolving network with the addition and deletion of nodes. It was found that networks of debtor-creditor relationships are scale-free networks. When the impact of default was considered in networks of debtor-creditor relationships, it was found that the power-law distribution of degree is not changed by the event of default, but the exponent of power-law under the event of default is less than the situation without the event of default. Our results enrich the application of complex networks.

Phase Transitions in Ising Model Defined on Complex Networks

In this work, we consider an Ising model which allows spin-spin interaction in the systems. We assume that two-level quantum systems are randomly located in N nodes of a complex annealed scale-free network described by the Barabasi-Albert model. It is defined by the power-law degree distribution of nodes. We consider the mean-field approach to the system described by the Ising Hamiltonian. At a certain level, the system is totally characterized by the order parameter Sz. It contains a critical inverse temperature β, which depends on parameter ζ2 as the ratio of the second to the first moment of the degree distribution. We have found that for ζ2, that exceeds its critical value ζ2,c, high temperature phase transition occurs that can be explained by the hubs and clusters which appear in scale-free networks.

Preferential attachment hypergraph with high modularity

AbstractNumerous works have been proposed to generate random graphs preserving the same properties as real-life large-scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist, and also, just a few models allow to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law, and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena.

Efficiently generating geometric inhomogeneous and hyperbolic random graphs

AbstractHyperbolic random graphs (HRGs) and geometric inhomogeneous random graphs (GIRGs) are two similar generative network models that were designed to resemble complex real-world networks. In particular, they have a power-law degree distribution with controllable exponent $\beta$ and high clustering that can be controlled via the temperature $T$ .We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to $T = 0$ . We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, that is, they involve no approximation.Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input.Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straightforward inclusion does not hold in practice. However, the difference is negligible for most use cases.

Topology and Geometry of the Third-Party Domains Ecosystem

Over the years, web content has evolved from simple text and static images hosted on a single server to a complex, interactive and multimedia-rich content hosted on different servers. As a result, a modern website during its loading time fetches content not only from its owner's domain but also from a range of third-party domains providing additional functionalities and services. Here, we infer the network of the third-party domains by observing the domains' interactions within users' browsers from all over the globe. We find that this network possesses structural properties commonly found in complex networks, such as power-law degree distribution, strong clustering, and small-world property. These properties imply that a hyperbolic geometry underlies the ecosystem's topology. We use statistical inference methods to find the domains' coordinates in this geometry, which abstract how popular and similar the domains are. The hyperbolic map we obtain is meaningful, revealing the large-scale organization of the ecosystem. Furthermore, we show that it possesses predictive power, providing us the likelihood that third-party domains are co-hosted; belong to the same legal entity; or merge under the same entity in the future in terms of company acquisition. We also find that complementarity instead of similarity is the dominant force driving future domains' merging. These results provide a new perspective on understanding the ecosystem's organization and performing related inferences and predictions.

Adding links on minimum degree and longest distance strategies for improving network robustness and efficiency.

Many real-world networks characterized by power-law degree distributions are extremely vulnerable against malicious attacks. Therefore, it is important to obtain effective methods for strengthening the robustness of the existing networks. Previous studies have been discussed some link addition methods for improving the robustness. In particular, two effective strategies for selecting nodes to add links have been proposed: the minimum degree and longest distance strategies. However, it is unclear whether the effects of these strategies on the robustness are independent or not. In this paper, we investigate the contributions of these strategies to improving the robustness by adding links in distinguishing the effects of degrees and distances as much as possible. Through numerical simulation, we find that the robustness is effectively improved by adding links on the minimum degree strategy for both synthetic trees and real networks. As an exception, only when the number of added links is small, the longest distance strategy is the best. Conversely, the robustness is only slightly improved by adding links on the shortest distance strategy in many cases, even combined with the minimum degree strategy. Therefore, enhancing global loops is essential for improving the robustness rather than local loops.

Turbulence and heat release rate network structure in hydrogen-enriched combustion

Complex network theory is used to analyze the spatiotemporal dynamics of the PRECCINSTA swirl burner, operating on hydrogen-methane fuel blends. At a power setting of 15 kW with equivalence ratio of 0.8 and hydrogen fuel fraction (HFF) ranging from 0% to 80%, period-1 and period-2 limit cycle oscillations as well as chaotic oscillations were observed. A turbulence network was constructed from the vorticity data obtained with particle image velocimetry. In addition, a heat release rate (HRR) correlation network was constructed from chemiluminescence images. Although the two networks concern a common thermoacoustic system, both exhibit significant differences: the turbulence network displays power law degree distribution, maintains small world property for all HFFs and is scale-free only in the absence of hydrogen enrichment. The HRR correlation network does not feature these properties, but hints at an asymmetric coupling between the heat release rate and the acoustic pressure for all HFFs. Furthermore, the HRR network is responsive to changes in HFF and the corresponding shifts in the dynamical state as well as in the root-mean-square of acoustic pressure. On the contrary, the turbulence network displays no such sensitivity and its properties are almost constant in the upper HFF range. It exhibits stationary hub structures for all the fuel blends tested, whereas the HRR correlation network is hub-free.

A new analysis of flow noise outside the time-frequency representation using graph-based feature extraction

Among various strategies to analyze spatiotemporal aero-hydro acoustic field, complex networks are a novel technique to deal with the acoustic pressure signals (APSs) which can fully reflect the inherent structure of the time series into complex networks. In this study first, sound generated from a low Mach number and turbulent flow around a three-dimensional circular cylinder is simulated. Then, using the complex network algorithm, APSs are transformed into natural visibility graphs (NVGs), and, their hidden signatures (macroscopic and microscopic characteristics) are unveiled using the topological metrics of the NVG. Later, spatial variations of 11 network metrics associated with 76 receiver signals distributed around the cylinder are explored and a bridge is built between these variations and their physical interpretations. The results show that all network properties corresponding to receiver signals located at a constant angular position are independent of the radial direction. Moreover, irrespective of the APSs properties, the power-law degree distribution is a feature shared by all networks, suggesting that it is a universal characteristic and highlights systems' self-organization and self-similarity characteristics in the sound field. Finally, physical interpretation of graph structures indicates that graph-based feature extraction enables identifying, distinguishing, and exploring underlying sound field dynamics in more detail.

Friend of a friend models of network growth.

One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many biological, physical and social systems, however, interactions between individuals depend only on local information. Here, we investigate a truly local model of network formation—based on the idea of a friend of a friend—with the following rule: individuals choose one node at random and link to it with probability p, then they choose a neighbour of that node and link with probability q. Our model produces power-laws with empirical exponents ranging from 1.5 upwards and clustering coefficients ranging from 0 up to 0.5 (consistent with many real networks). For small p and q = 1, the model produces super-hub networks, and we prove that for p = 0 and q = 1, the proportion of non-hubs tends to 1 as the network grows. We show that power-law degree distributions, small world clustering and super-hub networks are all outcomes of this, more general, yet conceptually simple model.

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.

The role of connectivity on COVID-19 preventive approaches.

Preventive and modeling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdős-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.

The structure and information spread capability of the network formed by integrated fitness apps

PurposeIn this article we aim to understand how the network formed by fitness tracking devices and associated apps as a subset of the broader health-related Internet of things is capable of spreading information.Design/methodology/approachThe authors used a combination of a content analysis, network analysis, community detection and simulation. A sample of 922 health-related apps (including manufacturers' apps and developers) were collected through snowball sampling after an initial content analysis from a Google search for fitness tracking devices.FindingsThe network of fitness apps is disassortative with high-degree nodes connecting to low-degree nodes, follow a power-law degree distribution and present with low community structure. Information spreads faster through the network than an artificial small-world network and fastest when nodes with high degree centrality are the seeds.Practical implicationsThis capability to spread information holds implications for both intended and unintended data sharing.Originality/valueThe analysis confirms and supports evidence of widespread mobility of data between fitness and health apps that were initially reported in earlier work and in addition provides evidence for the dynamic diffusion capability of the network based on its structure. The structure of the network enables the duality of the purpose of data sharing.