Scale-free Property Research Articles

Exploring Spatial Dynamics and Network Structures in Inbound Tourism Flow

Drawing on the theoretical frameworks of structural functionalism and relational research perspectives, this study meticulously constructs and analyzes China's inbound tourism flow network spanning the years 2001 to 2023. Employing a diverse array of analytical tools such as the small-world model, rank-size model, structural equivalence model, core-periphery model, and various centrality metrics, the research delves into the structural characteristics and evolution patterns of China's inbound tourism flow network within a comprehensive spatial-temporal framework. Key findings include: 1) Small-world and scale-free properties with tourist flows concentrated in pivotal provinces. 2) Persistence of a U-shaped pattern in inbound tourism, with robust activity in eastern and western regions. 3) Presence of a core-periphery structure, with Beijing, Shanghai, and Guangdong as national hubs. This research enhances understanding of tourism industry spatial organization, offering insights for policymakers and stakeholders in tourism development.

Constructing the biomolecular networks associated with diabetic nephropathy and dissecting the effects of biomolecule variation underlying pathogenesis.

Diabetic nephropathy (DN) is a common and serious complication of diabetes, contributing significantly to patient mortality. Complication of DN (CDN) ranks as the second leading cause of end-stage renal disease globally. To address this, understanding the genetic regulation underlying DN is crucial for personalized treatment strategies. In this study, we identified genes and lncRNAs associated with diabetes and diabetic nephropathy constructing a DN-related lncRNA-mRNA network (DNLMN). This network, characterized by scale-free biomolecular properties, generated through the study of topological properties, elucidates key regulatory interactions. Enrichment analysis of important network modules revealed critical biological processes and pathways involved in DN pathogenesis. In the second step, we investigated the differential expression and co-expression of hub nodes in diseased and normal individuals, identifying lncRNA-mRNA relationships implicated in disease regulation. Finally, we gathered DN-related single nucleotide polymorphisms (SNPs) and lncRNAs from the LincSNP 3.0 database. The DNLMN encompasses SNP-associated lncRNAs, and transcription factors (TFs) linked to differentially expressed lncRNAs between diseased and normal samples. These results underscore the significance of biomolecular networks in disease progression and highlighting the role of biomolecular variability contributes to personalized disease phenotyping and treatment.

Elucidation of characteristics of networks where every node has its own lifetime

Growth is regarded as an important mechanism for explaining the structures of real networks. However, when the increase in the number of nodes is suppressed owing to their lifetime, the growth property alone is not sufficient to explain even fundamental network properties, such as the scale-free property. In this paper, we propose a network model that considers the lifetime of nodes and the excess addition of local internal links as a mechanism that supports network structures. By investigating the model network, we aimed to elucidate the network characteristics supported by local interactions between nodes via their common neighbors even when the rates of node addition and deletion were balanced. We found that the stationary state of the number of nodes is characterized by a scale-free property with the power-law exponent γ≃1 and localization of the peaks at l=2 in the distance distributions of neighboring nodes (DDN) as the node degree k increases. The specific behavior of the DDN explains the very slow decrease in the clustering strength C(k) with k compared with the normal behavior C(k)∼k−1 and the accelerated growth of the neighborhood graph of each node. Moreover, we showed that some real networks share local structures similar to those of the model network. These findings suggest that the same mechanism as that of the proposed model plays an essential role in supporting the local structures of some real networks.

Core allocation to minimize total flow time in a multicore system in the presence of a processing time constraint

Data centers are a vital and fundamental infrastructure component of the cloud. The requirement to execute a large number of demanding jobs places a premium on processing capacity. Parallelizing jobs to run on multiple cores reduces execution time. However, there is a decreasing marginal benefit to using more cores, with the speedup function quantifying the achievable gains. A critical performance metric is flow time. Previous results in the literature derived closed-form expressions for the optimal allocation of cores to minimize total flow time for a power-law speedup function if all jobs are present at time 0. However, this work did not place a constraint on the makespan. For many diverse applications, fast response times are essential, and latency targets are specified to avoid adverse impacts on user experience. This paper is the first to determine the optimal core allocations for a multicore system to minimize total flow time in the presence of a completion deadline (where all jobs have the same deadline). The allocation problem is formulated as a nonlinear optimization program that is solved using the Lagrange multiplier technique. Closed-form expressions are derived for the optimal core allocations, total flow time, and makespan, which can be fitted to a specified deadline by adjusting the value of a single Lagrange multiplier. Compared to the unconstrained problem, the shortest job first property for optimal allocation is maintained; however, a number of other properties require revising and other properties are only retained in a modified form (such as the scale-free and size-dependence properties). It is found that with a completion deadline the optimal solution may contain groups of simultaneous completions. In general, all possible patterns of single- and group-completion need to be considered, producing an exponential search space. However, the paper determines analytically that the optimal completion pattern consists of a sequence of single completions followed by a single group of simultaneous completions at the end, which reduces the search space dimension to being linear. The paper validates the Lagrange multiplier approach by verifying constraint qualifications.

Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library scikit-tda, and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Identifying highly connected sites for risk-based surveillance and control of cucurbit downy mildew in the eastern United States.

Surveillance is critical for the rapid implementation of control measures for diseases caused by aerially dispersed plant pathogens, but such programs can be resource-intensive, especially for epidemics caused by long-distance dispersed pathogens. The current cucurbit downy mildew platform for monitoring, predicting and communicating the risk of disease spread in the United States is expensive to maintain. In this study, we focused on identifying sites critical for surveillance and treatment in an attempt to reduce disease monitoring costs and determine where control may be applied to mitigate the risk of disease spread. Static networks were constructed based on the distance between fields, while dynamic networks were constructed based on the distance between fields and wind speed and direction, using disease data collected from 2008 to 2016. Three strategies were used to identify highly connected field sites. First, the probability of pathogen transmission between nodes and the probability of node infection were modeled over a discrete weekly time step within an epidemic year. Second, nodes identified as important were selectively removed from networks and the probability of node infection was recalculated in each epidemic year. Third, the recurring patterns of node infection were analyzed across epidemic years. Static networks exhibited scale-free properties where the node degree followed a power-law distribution. Betweenness centrality was the most useful metric for identifying important nodes within the networks that were associated with disease transmission and prediction. Based on betweenness centrality, field sites in Maryland, North Carolina, Ohio, South Carolina and Virginia were the most central in the disease network across epidemic years. Removing field sites identified as important limited the predicted risk of disease spread based on the dynamic network model. Combining the dynamic network model and centrality metrics facilitated the identification of highly connected fields in the southeastern United States and the mid-Atlantic region. These highly connected sites may be used to inform surveillance and strategies for controlling cucurbit downy mildew in the eastern United States.

Power Law in Deep Neural Networks: Sparse Network Generation and Continual Learning With Preferential Attachment.

Training deep neural networks (DNNs) typically requires massive computational power. Existing DNNs exhibit low time and storage efficiency due to the high degree of redundancy. In contrast to most existing DNNs, biological and social networks with vast numbers of connections are highly efficient and exhibit scale-free properties indicative of the power law distribution, which can be originated by preferential attachment in growing networks. In this work, we ask whether the topology of the best performing DNNs shows the power law similar to biological and social networks and how to use the power law topology to construct well-performing and compact DNNs. We first find that the connectivities of sparse DNNs can be modeled by truncated power law distribution, which is one of the variations of the power law. The comparison of different DNNs reveals that the best performing networks correlated highly with the power law distribution. We further model the preferential attachment in DNNs evolution and find that continual learning in networks with growth in tasks correlates with the process of preferential attachment. These identified power law dynamics in DNNs can lead to the construction of highly accurate and compact DNNs based on preferential attachment. Inspired by the discovered findings, two novel applications have been proposed, including evolving optimal DNNs in sparse network generation and continual learning tasks with efficient network growth using power law dynamics. Experimental results indicate that the proposed applications can speed up training, save storage, and learn with fewer samples than other well-established baselines. Our demonstration of preferential attachment and power law in well-performing DNNs offers insight into designing and constructing more efficient deep learning.

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

To investigate the relationship between histological properties and thermal conductivities of binary self-assembled/self-organized fractal materials fabricated by the mixed diffusion of filler particles, the particle group distribution of the filler particles was analyzed. Unlike conventional research on particle size distribution, we performed an analysis that focuses on interactions and connectivity between particles from the perspective of the Barabasi-Albert model. In three complex network systems of β-Si3N4 (SN)/austenitic stainless steel (SUS), SN/piezoelectric polyvinylidene fluoride (PVDF), and BaTiO3 (BT)/PVDF, the size distribution of secondary particles was a power-law distribution until the particle group grew relatively large. In the SN/SUS and SN/PVDF systems, a crossover phenomenon was observed in which the order distribution exhibited a power-law in the region where the particle group area was small, and as the particle group became larger, the order distribution became exponential distribution. On the other hand, the BT/PVDF system deviated from the power law distribution as the particle group area increased but did not exhibit an exponential distribution. The characteristics of the particle group distribution of these filler particles were closely related to thermal conductivity, indicating that the connection of particle groups was important. Furthermore, the relationship between the multifractal capacitance dimension, which is strongly correlated with the distance between the particle groups, and the total number of filler particle groups suggests that the texture of these composite material systems may have both small-world and scale-free properties. We also focused on the relationship between the multifractal and complex network properties of the three particle groups. As a result, a correlation was found between the slope γ, which reflects the characteristics of the power distribution, and the thermodynamic parameter α (corresponding to internal energy change) obtained from multifractals. In particular, the smaller the change in γ relative to the change in α, the more pronounced the bonding of particles and particle groups, while the larger change in γ suggested the dispersion of particle groups.

Power law of path multiplicity in complex networks.

Complex networks describe a wide range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a vital role in network science. Rather than focusing on the path length or path centrality, here we draw attention to the path multiplicity related to decision-making efficiency, which is defined as the number of shortest paths between node pairs and thus characterizes the routing choice diversity. Notably, through extensive empirical investigations from this new perspective, we surprisingly observe a "hesitant-world" feature along with the "small-world" feature and find a universal power-law of the path multiplicity, meaning that a small number of node pairs possess high path multiplicity. We demonstrate that the power-law of path multiplicity is much stronger than the power-law of node degree, which is known as the scale-free property. Then, we show that these phenomena cannot be captured by existing classical network models. Furthermore, we explore the relationship between the path multiplicity and existing typical network metrics, such as average shortest path length, clustering coefficient, assortativity coefficient, and node centralities. We demonstrate that the path multiplicity is a distinctive network metric. These results expand our knowledge of network structure and provide a novel viewpoint for network design and optimization with significant potential applications in biological, social, and man-made networks.

Exploring scale-free networks: Survey on autonomous system dynamics and connectivity analysis

The global Internet is continuously developing; however, it is becoming more complex with time owing to the introduction of new nodes and links among autonomous systems (ASes). The network links among ASes appear and disappear, especially when the shortest path is required or a low-cost upstream Internet service provider (ISP) is a prerequisite. Understanding the Internet dynamics is critical for improving Internet characteristic analysis. In this work, we reviewed the existing studies from the last two decades on AS network topology as well as relations and routing among ASes. Similarly, we measured the link value differences within Russia and Central Asian ASes using the Barabasi–Albert (BA) model. Our analysis results show that in the last two years, the number of newly added links among 5377 ASes is 65,782. Further, the results show that the ASes with a high network degree in terms of high connectivity or preferential attachment approach are those used by the largest telecom companies in Russia and Central Asian regions. This survey paper aimed to determine whether the Internet AS graphs in these regions adhere to scale-free network properties, and we further examined the growth patterns of node connectivity within these regions.

Cooperation emerged and survived in scale-free networks in co-evolution and betrayer-prevailing circumstances

How did cooperation emerge and persist while betrayal was beneficial for individuals? Previous studies suggested that network reciprocity was a promising explanation. However, these studies usually analyzed cooperation performances of different types of networks separately and/or statically, thus failing to fully capture the co-evolution and interaction features in our history. We proposed a mechanism that analyzed the cooperation level of different types of networks under co-evolutionary circumstances of cooperation and heterogeneous networks. The paper adopted the prisoner's dilemma game and analyzed Erdos-Renyi (ER) random networks, Watts Strogatz (WS) small-world networks, and Barabasi-Albert (BA) scale-free networks. In this study, these networks were interconnected and continuously grew after gaming evolutions were stable. And the growth versions of WS and ER respectively were proposed that maintained their topology features. Comprehensive experimental results showed that high-level cooperation emerged and was maintained in scale-free networks. This advantage was strengthened with networks grew from a small scale to a middle scale. Moreover, once most nodes of a scale-free network evolved to be cooperators, the group cooperation they formed were able to survive in betrayer-prevailing and high betrayal temptation environments. These findings may deepen our understanding of the relationship between how cooperation evolved and why many social networks exhibited scale-free properties.

Lexical Characterization of Ancient and Modern Chinese Combined with Semantic Association Network Modeling

Abstract This paper explores the linguistic features of ancient and modern Chinese, focuses on capturing the knowledge of the relevant domains of ancient and contemporary Chinese using semantic models, and carries out the corresponding semantic resource extraction and semantic representation through the resource expression mechanism in the framework of the Semantic Association Network Model (SANM), and then analyzes the historical evolution of the lexicalization patterns of the Chinese language and the linguistic features of the Chinese language in different periods. In the historical evolution of Chinese lexicalization patterns, it is found that the distribution of lexicalization patterns of ancient Chinese table-cutting action lexical items is [action+object] > [action+method] > [action result] > [action+tool], and the distribution of lexicalization patterns of modern Chinese table-cutting action lexical items is [action+method] > [action+tool] > [action+result] > [action+object]. The linguistic features of different periods show that all networks have small-world properties and scale-free properties, and the statistical parameters of the networks in each period are relatively close to each other, with the modern network having the most significant C (8.59) and the smallest L (0.92) and γ (0.40). Ancient and modern Chinese words and phrases with relational word collocations in the interval [0,23] have the most extensive and densest distribution of relational words. These data present the similarities and differences between linguistic features between ancient and modern Chinese, which is significant for studying ancient and modern Chinese.

Robustness of the International Wheat Trade Network

Grain is the material basis for human survival and development, wheat is one of the three significant grains, and the robustness of the wheat trade has seriously affected world grain security. In the paper, we analyze the robustness of the International Wheat Trade Network (IWTN) from three perspectives: global, regional, and national. We quantify the topological properties and evolution characteristics of IWTN from 1987 to 2020, and analyze the stability of IWTN using random attacks and target attacks. The import satisfaction of major wheat trading countries and trade communities is quantified through import stability indicators. Firstly, the results show that IWTN satisfies the scale-free property and that global wheat trade transactions continue to increase. Secondly, IWTN under random attack forms a “convex” curve regarding network efficiency. It shows that IWTN has better resistance to external shocks, and higher robustness. However, under the targeted attack, the network collapses when the node failure rate reaches 40%. Regardless of the attack mode, the decreasing trend of network efficiency and connectivity is the same in different years as the number of failed nodes gradually increases, and no year shows outstanding stability. Thirdly, different communities in the wheat trade are more satisfied with the wheat imports of their internal countries, and most of the wheat trade occurs within the same trading community. Fourthly, among the top five global wheat importers in 2020, Italy and Turkey have diversified sources of imports, but trade imports are relatively concentrated. In contrast, China, Egypt and Indonesia have relatively balanced wheat trade imports from their respective trading countries and are less at risk of being affected in the event of supply risks.

Empirical Network Structure of Malicious Programs

A modern binary executable is a composition of various types of networks. Control flow graphs are a commonly used representation of an executable program used for classification tasks. Control flow and term frequency representations are widely adopted, but provide only a partial view of program semantics and present challenges to increases in resolution. By performing a quantitative analysis of program networks, we enable the identification of patterns within these features that are correlated to structure. This allows for increases in feature resolution and pattern recognition in classification tasks. These are necessary steps in order to obtain greater explainability in classification results. We demonstrate the presence of Scale-Free properties of network structure for program data dependency and control flow graphs, and show that data dependency graphs also have Small-World structural properties. We show that program data dependency graphs have a degree correlation that is structurally disassortative, and that control flow graphs have a neutral degree assortativity, indicating the use of random graphs to model the structural properties of program control flow graphs would show increased accuracy. An increase in feature resolution allows for the structural

DHGAT: Hyperbolic representation learning on dynamic graphs via attention networks

Hyperbolic graph embedding has garnered significant attention in a wide range of downstream applications. This is because hyperbolic geometry provides a valuable mapping tool, whereby the scale-free or hierarchical properties of complex networks can be naturally reflected as hyperbolic metric properties. Despite this, most advancements have focused on learning hyperbolic representations of static graphs, the potential advantages of hyperbolic metrics in dynamic graphs embedding have not been fully exploited. To fully harness the properties of hyperbolic space, we propose DHGAT11https://github.com/Lihaogx/DHGAT., a dynamic hyperbolic graph attention network with a novel architecture that designs a spatiotemporal self-attention mechanism based on hyperbolic distance. DHGAT maps dynamic graphs into the hyperbolic space, generates spatiotemporal self-attention of nodes, and directly aggregates weighted node representations without the tangent space. This is achieved by using the Einstein gyromidpoints, which reduces distortions and preserves manifold properties. The results of experiments on real-world datasets demonstrate that DHGAT performs exceptionally well in multi-step link prediction tasks, particularly in predicting new links compared to the baselines.

Analysis of the Evolution of Scale-Free Properties in the Complex Network of American White Moths in Liaoning Area

Analysis of the Evolution of Scale-Free Properties in the Complex Network of American White Moths in Liaoning Area

Emergence of dense scale-free networks and simplicial complexes by random degree-copying

Abstract Many real-world networks exhibit dense and scale-free properties, that is, the amount of connections among the nodes is large and the degree distribution follows a power-law P(k)∼k−γ. In particular, for dense networks γ∈(1,2]. In the literature, numerous network growth models have been proposed with the aim to reproduce structural properties of these networks. However, most of them are not capable of generating dense networks and power-laws with exponents in the correct range of values. In this research, we provide a new network growth model that enables the construction of networks with degree distributions following a power law with exponents ranging from one to an arbitrary large number. In our model, the growth of the network is made using the well-known Barabási–Albert model, that is, by nodes and links addition and preferential attachment. The amount of connections with which each node is born, can be fixed or depending of the network structure incorporating a random degree-copying mechanism. Our results indicate that if degree-copying mechanism is applied most of the time, then the resulting degree distribution has an exponent tending to one. Also, we show that the resulting networks become denser as γ→1, in consequence their clustering coefficient increases and network diameter decreases. In addition, we study the emergence of simplicial complexes on the resulting networks, finding that largest simplicial dimension appears as γ decreases.

Graph-Theoretical Analysis of Biological Networks: A Survey

Biological networks such as protein interaction networks, gene regulation networks, and metabolic pathways are examples of complex networks that are large graphs with small-world and scale-free properties. An analysis of these networks has a profound effect on our understanding the origins of life, health, and the disease states of organisms, and it allows for the diagnosis of diseases to aid in the search for remedial processes. In this review, we describe the main analysis methods of biological networks using graph theory, by first defining the main parameters, such as clustering coefficient, modularity, and centrality. We then survey fundamental graph clustering methods and algorithms, followed by the network motif search algorithms, with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function that is carried out by that small network, and discovering such a function provides an insight into the overall function of the organism. Lastly, we review network alignment algorithms that find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor, and finding such a relationship may help researchers to derive ancestral relationships and to predict the future evolution of organisms to enable the design of new drugs. We provide a review of the research studies in all of these methods, and conclude using the current challenging areas of biological network analysis, and by using graph theory and parallel processing for high performance analysis.

Tracing the birth of structural domains from loops during protein evolution

The structures and functions of proteins are embedded into the loop scaffolds of structural domains. Their origin and evolution remain mysterious. Here, we use a novel graph-theoretical approach to describe how modular and non-modular loop prototypes combine to form folded structures in protein domain evolution. Phylogenomic data-driven chronologies reoriented a bipartite network of loops and domains (and its projections) into ‘waterfalls’ depicting an evolving ‘elementary functionome’ (EF). Two primordial waves of functional innovation involving founder ‘p-loop’ and ‘winged-helix’ domains were accompanied by an ongoing emergence and reuse of structural and functional novelty. Metabolic pathways expanded before translation functionalities. A dual hourglass recruitment pattern transferred scale-free properties from loop to domain components of the EF network in generative cycles of hierarchical modularity. Modeling the evolutionary emergence of the oldest P-loop and winged-helix domains with AlphFold2 uncovered rapid convergence towards folded structure, suggesting that a folding vocabulary exists in loops for protein fold repurposing and design.

The Achilles heel of interconnected user networks: Network firms and the vulnerability of rapid decline

Digital technologies have amplified firms' ability to gain and sustain competitive advantages by leveraging network effects and large user bases. They allow cheaper and better building, scaling, and operation of user networks, more efficient data collection, lower transaction costs, and ever-stronger scale advantages. Yet, the seemingly stable competitive advantage of large-scale user networks may have an “Achilles heel” that creates a strategic vulnerability. We examine this overlooked effect by studying how structural network characteristics affect the risk of rapid decline after users start to depart. We find that for user networks with small-world and scale-free properties, the departure of a few influential users can prompt strong negative network effects and accelerate the speed of a decline. To arrive at these insights, we use an analytical approach inspired by the computational networks literature to assess the impact of different structural characteristics on the likelihood of rapid collapse. Our research enriches the platform and network literature by providing fresh insights into the vulnerabilities of interconnected user networks, highlighting the risk of rapid decline. We also suggest practical implications for firms that depend on such networks for a competitive edge.