Scale-free Network Structure Research Articles

Quantification and comparison of hierarchy in Public Transport Networks

Network hierarchy describes the relative arrangement of network elements and reflects its fundamental structure. We propose a multi-dimensional topology-based method for quantifying and comparing the extent to which different Public Transport Networks (PTNs) exhibit a hierarchical structure. The proposed method considers the uneven distribution of node importance with different definitions (e.g., degree centrality and betweenness centrality) in a PTN, the clustering of nodes and the node connection patterns. We apply the developed method on 63 high-capacity PTNs worldwide using General Transit Feed Specification (GTFS) data. In addition to global indicators, we use the goodness-of-fit between the probability density function of local indicators and a skew-normal distribution to quantify the extent of PTN hierarchy. Results show that the scale-free network structure and preferential attachment do not vary much across PTNs. In contrast, stop accessibility and traffic intermediacy vary considerably across PTNs as reflected by the closeness centrality and betweenness centrality distributions. Lastly, metro systems exhibit a more hierarchical structure than their tram and Bus Rapid Transit (BRT) counterparts. This work makes a first step towards a better mapping and comparison of different PTNs, which can assist academics and practitioners in better (re)designing and planning the PTNs of the future.

Dynamic survivability in oscillator systems

Whether the dynamic systems can display normal performance or complete key mission is the hot spot in recent years. In accordance with this, dynamic survivability is defined for the first time and mission-completion-probability is given as an index in this study. Taking the behavior of diffusively coupled oscillator systems with Erdös-Rényi random graph and Barabási-Albert scale-free network structures as examples, we show the network structures, systems’ parameters and attack strategies exhibit a profound influence on the dynamic survivability. Erdös-Rényi random graph and Barabási-Albert scale-free systems display better or worse dynamic survivability under different attack strategies respectively. Our outcomes fill the gap in the survivability study and are helpful for enhancing the dynamic survivability of real systems.

Stratified structure of fractal scale-free networks generated by local rules

Fractal networks are a special class of self-organized networks in the real world. Several network models have been proposed to explain fractality, but most of them are intentionally designed to generate self-similar structures. However, considering that most real-world networks appear to be self-organized by random and local events, random phenomena occurring in networks are expected to be more relevant for explaining fractality than intentional design. In this study, we focus on the process of the formation of stratified structures to clarify the mechanism by which local rules generate fractal properties. First, we numerically show that fractal networks are generated by local and random events by investigating two model networks, the n-step random walk (RW) model and the intermediary process (IP) model. Second, we investigate stratified structures, including the power-law forms of frequency distributions of offspring at each depth l, where the depth l is defined as the distance from the root vertices to each vertex in a family tree embedded in the resulting networks. As a result, we find that the local structures defined on each layer, such as the birth rate factor Bl, characterize the growth of stratified structures of the model networks. Finally, to demonstrate a crucial role of Bl in the emergence of fractality, we showed that a general algorithm based on the concept of birth rate factor can certainly produce fractal small-world scale-free trees. Surprisingly, random processes such as random walks induce local structures that support stratified, fractal, and small-world (or non-small-world) networks.

Mean-field theory of superradiant phase transition in complex networks.

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k^{-γ}] degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of γ, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in z direction with increasing γ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.

Evolution of networks of protein domain organization

Domains are the structural, functional and evolutionary units of proteins. They combine to form multidomain proteins. The evolutionary history of this molecular combinatorics has been studied with phylogenomic methods. Here, we construct networks of domain organization and explore their evolution. A time series of networks revealed two ancient waves of structural novelty arising from ancient ‘p-loop’ and ‘winged helix’ domains and a massive ‘big bang’ of domain organization. The evolutionary recruitment of domains was highly modular, hierarchical and ongoing. Domain rearrangements elicited non-random and scale-free network structure. Comparative analyses of preferential attachment, randomness and modularity showed yin-and-yang complementary transition and biphasic patterns along the structural chronology. Remarkably, the evolving networks highlighted a central evolutionary role of cofactor-supporting structures of non-ribosomal peptide synthesis pathways, likely crucial to the early development of the genetic code. Some highly modular domains featured dual response regulation in two-component signal transduction systems with DNA-binding activity linked to transcriptional regulation of responses to environmental change. Interestingly, hub domains across the evolving networks shared the historical role of DNA binding and editing, an ancient protein function in molecular evolution. Our investigation unfolds historical source-sink patterns of evolutionary recruitment that further our understanding of protein architectures and functions.

Network structure, portfolio diversification and systemic risk

We investigate the effect of portfolio diversification on banking systemic risk, where the network effect is incorporated. We analyze three kinds of interbank networks, namely, random networks, small-world networks and scale-free networks. We show that the effect of portfolio diversification on banking systemic risk depends on interbank network structures and shock types. First, systemic risk increases first and then reduces with the increase of the level of portfolio diversification in the case of the individual shock. Second, in the case of the systemic shock, systemic risk reduces with the increases of the level of portfolio diversification. Third, banking systems with scale-free network structures are the most stable, and those with small-world network structures are the most vulnerable.

Agent-based evolving network modeling: a new simulation method for modeling low prevalence infectious diseases

Agent-based network modeling (ABNM) simulates each person at the individual-level as agents of the simulation, and uses network generation algorithms to generate the network of contacts between individuals. ABNM are suitable for simulating individual-level dynamics of infectious diseases, especially for diseases such as HIV that spread through close contacts within intricate contact networks. However, as ABNM simulates a scaled-version of the full population, consisting of all infected and susceptible persons, they are computationally infeasible for studying certain questions in low prevalence diseases such as HIV. We present a new simulation technique, agent-based evolving network modeling (ABENM), which includes a new network generation algorithm, Evolving Contact Network Algorithm (ECNA), for generating scale-free networks. ABENM simulates only infected persons and their immediate contacts at the individual-level as agents of the simulation, and uses the ECNA for generating the contact structures between these individuals. All other susceptible persons are modeled using a compartmental modeling structure. Thus, ABENM has a hybrid agent-based and compartmental modeling structure. The ECNA uses concepts from graph theory for generating scale-free networks. Multiple social networks, including sexual partnership networks and needle sharing networks among injecting drug-users, are known to follow a scale-free network structure. Numerical results comparing ABENM with ABNM estimations for disease trajectories of hypothetical diseases transmitted on scale-free contact networks are promising for application to low prevalence diseases.

Zaihoum Threshold of Credit Risk Contagion within Enterprise Groups

Liu, Y.M.; Cui, Y.Q., and Yu, B.L., 2020. Zaihoum threshold of credit risk contagion within enterprise groups. In: Guido Aldana, P.A. and Kantamaneni, K. (eds.), Advances in Water Resources, Coastal Management, and Marine Science Technology. Journal of Coastal Research, Special Issue No. 104, pp. 198–202. Coconut Creek (Florida), ISSN 0749-0208.In view of the fact that the assessment of group credit risk is more difficult and complex than that of general enterprises due to the complex and concealed relationship within the enterprise group, and that the structural relationship among the members of the enterprise group is consistent with the scale-free network structure, the mechanism of credit risk contagion within the enterprise group is analyzed by applying grey theory and probability theory under the scale-free network structure. The research shows that the contagion threshold of credit risk within an enterprise group is related to the maximum contagion capacity of the member companies within the group. The stronger the maximum contagion capacity, the smaller the contagion threshold, the more likely the credit risk is to be contagious among the members within the group. The contagion threshold of credit risk among members of a group is independent of the size of the group.

Development of the Theory of Six Value Aggregation Paths in Network Modeling for Spatial Analyses

The dynamic development of spatial structures entails looking for new methods of spatial analysis. The aim of this article is to develop a new theory of space modeling of network structures according to six value aggregation paths: minimum and maximum value difference, minimum and maximum value decrease, and minimum and maximum value increase. The authors show how values presenting (describing) various phenomena or states in urban space can be designed as network structures. The dynamic development of spatial structures entails looking for new methods of spatial analysis. This study analyzes these networks in terms of their nature: random or scale-free. The results show that the paths of minimum and maximum value differences reveal one stage of the aggregation of those values. They generate many small network structures with a random nature. Next four value aggregation paths lead to the emergence of several levels of value aggregation and to the creation of scale-free hierarchical network structures. The models developed according to described theory present the quality of urban areas in various versions. The theory of six paths of value combination includes new measuring tools and methods which can impact quality of life and minimize costs of bad designs or space destructions. They are the proper tools for the sustainable development of urban areas.

Synaptic Failure Differentially Affects Pattern Formation in Heterogenous Networks.

The communication of neurons is primarily maintained by synapses, which play a crucial role in the functioning of the nervous system. Therefore, synaptic failure may critically impair information processing in the brain and may underlie many neurodegenerative diseases. A number of studies have suggested that synaptic failure may preferentially target neurons with high connectivity (i.e., network hubs). As a result, the activity of these highly connected neurons can be significantly affected. It has been speculated that anesthetics regulate conscious state by affecting synaptic transmission at these network hubs and subsequently reducing overall coherence in the network activity. In addition, hubs in cortical networks are shown to be more vulnerable to amyloid deposition because of their higher activity within the network, causing decrease in coherence patterns and eventually Alzheimer’s disease (AD). Here, we investigate how synaptic failure can affect spatio-temporal dynamics of scale free networks, having a power law scaling of number of connections per neuron – a relatively few neurons (hubs) with a lot of emanating or incoming connections and many cells with low connectivity. We studied two types of synaptic failure: activity-independent and targeted, activity-dependent synaptic failure. We defined scale-free network structures based on the dominating direction of the connections at the hub neurons: incoming and outgoing. We found that the two structures have significantly different dynamical properties. We show that synaptic failure may not only lead to the loss of coherence but unintuitively also can facilitate its emergence. We show that this is because activity-dependent synaptic failure homogenizes the activity levels in the network creating a dynamical substrate for the observed coherence increase. Obtained results may lead to better understanding of changes in large-scale pattern formation during progression of neuro-degenerative diseases targeting synaptic transmission.

Macroprudential regulation for a dynamic Chinese banking system with a scale-free network

The frequent global financial crises in recent years show that it is necessary to implement macroprudential regulation for the banking system. At present, quantitative research on the macroprudential regulation for the dynamic Chinese banking network system is lacking, while the related studies in other countries have not considered the interbank network structure. Therefore, in the present paper, we construct a dynamic banking network model with a scale-free network and a dynamic macroprudential regulation model under four risk allocation mechanisms (CVaR, Incremental VaR, Shapley value EL, and ΔCoVaR) for the dynamic Chinese banking network system. Then, we conduct empirical research to study the effect of the macroprudential regulation model on the Chinese banking network system. Our results show that the Chinese banking network system was the most unstable in 2010 and that the average default probability decreased every year after the macroprudential regulation, indicating the effectiveness of the macroprudential regulation model. From the perspective of the scale-free network structure, we find that the intrinsic mechanism of macroprudential regulation is to rewire the interbank linkages from small banks to large banks with more interbank lending to prevent contagious risk, thereby improving the stability of the entire banking system. Moreover, the regulation effects of ΔCoVaR and CVaR mechanisms are found to be better than those of the other mechanisms. The regulation effect of ΔCoVaR is the most significant.

Improving short-term information spreading efficiency in scale-free networks by specifying top large-degree vertices as the initial spreaders.

The positive function of initially influential vertices could be exploited to improve spreading efficiency for short-term spreading in scale-free networks. However, the selection of initial spreaders depends on the specific scenes. The selection of initial spreaders needs to offer low complexity and low power consumption for short-term spreading. In this paper, we propose a selection strategy for efficiently spreading information by specifying a set of top large-degree vertices as the initially informed vertices. The essential idea behind the proposed selection strategy is to exploit the significant diffusion of the top large-degree vertices at the beginning of spreading. To evaluate the positive impact of initially influential vertices, we first build an information spreading model in the Barabási–Albert (BA) scale-free network; next, we design 54 comparative Monte Carlo experiments based on a benchmark strategy and the proposed selection strategy in different BA scale-free network structures. Experimental results indicate that (i) the proposed selection strategy can significantly improve spreading efficiency in the short-term spreading and (ii) both network size and number of hubs have a strong impact on spreading efficiency, while the number of initially informed vertices has a weak impact. The proposed selection strategy can be employed in short-term spreading, such as sending warnings or crisis information spreading or information spreading in emergency training or realistic emergency scenes.

Network-agent based model for simulating the dynamic spatial network structure of complex ecological systems

Non-spatial ecological networks provide insight into the organization and interaction between biological entities. More recently, biological dispersal is modelled using spatial networks, static sets of georeferenced habitat patches that connect based on a species’ maximum dispersal distance. However, dispersal is complex, where spatial patterns at the landscape scale emerge from interactions between ecological entities and landscape features at much finer individual scales. Agent-based modelling (ABM) is a computational representation of complex systems capable of capturing this complexity. Therefore, this study develops a network-ABM (N-ABM) that combines network and complex systems theory to simulate complex evolving spatial networks. The developed N-ABM approach is implemented on the case study of the emerald ash borer (EAB) bark beetle using geospatial datasets in Ontario, Canada. The N-ABM generates dynamic spatial network structures that emerge from interactions between the EAB and tree agents at the individual scale. The resulting networks are analyzed using graph theory measures. Analysis of the results indicates a relationship between preferential attachment in insect host selection and the emergent scale-free network structure. The N-ABM approach can be used to represent dynamic ecological networks and provides insight into how network structure emerges from EAB dispersal dynamics, useful for forest management.

Designing efficient hybrid strategies for information spreading in scale-free networks.

Designing a spreading strategy is one of the critical issues strongly affecting spreading efficiency in complex networks. In this paper, to improve the efficiency of information spreading in scale-free networks, we propose four hybrid strategies by combining two basic strategies, i.e. (i) the LS (in which information is preferentially spread from the large-degree vertices to the small-degree ones), and (ii) the SL (in which information is preferentially spread from the small-degree vertices to the large-degree ones). The objective in combining the two basic LS and SL strategies is to fully exploit the advantages of both strategies. To evaluate the spreading efficiency of the proposed four hybrid strategies, we first propose an information spreading model. Then, we introduce the details of the proposed hybrid strategies that are formulated by combining LS and SL. Third, we build a set of scale-free network structures by differently configuring the relevant parameters. In addition, finally, we conduct various Monte Carlo experiments to examine the spreading efficiency of the proposed hybrid strategies in different scale-free network structures. Experimental results indicate that the proposed hybrid strategies are effective and efficient for spreading information in scale-free networks.

Network structures and systems: I. Flows characteristics of complex networks

Structural and functional directions of complex network systems research are considered. The network system is defined as a complex network where flows occur. The classification of network systems is carried out on the basis of continuity and the level of orderliness of flows. Flow characteristics of network systems are introduced along with the structural characteristics of complex networks. The problem of critical loading of network components is studied. Problems of dimension and adequacy of models of network systems are considered. It is shown how the system's flow characteristics allow us to identify and exclude fictitious nodes and links from its structure and determine the hidden elements of the system. It was investigated how on the basis of the analysis of flows processes in the system the structure of scale-free networks changed not only during the growth stage, but also during the whole life cycle of the corresponding network system. The problem of isolated zones of network systems is considered and the algorithm is proposed for finding alternative ways for flows in order to bypass inaccessible components of the network.

Multilevel Evolutionary Algorithm that Optimizes the Structure of Scale-Free Networks for the Promotion of Cooperation in the Prisoner\u2019s Dilemma game

Understanding the emergence of cooperation has long been a challenge across disciplines. Even if network reciprocity reflected the importance of population structure in promoting cooperation, it remains an open question how population structures can be optimized, thereby enhancing cooperation. In this paper, we attempt to apply the evolutionary algorithm (EA) to solve this highly complex problem. However, as it is hard to evaluate the fitness (cooperation level) of population structures, simply employing the canonical evolutionary algorithm (EA) may fail in optimization. Thus, we propose a new EA variant named mlEA-CPD-SFN to promote the cooperation level of scale-free networks (SFNs) in the Prisoner’s Dilemma Game (PDG). Meanwhile, to verify the preceding conclusions may not be applied to this problem, we also provide the optimization results of the comparative experiment (EAcluster), which optimizes the clustering coefficient of structures. Even if preceding research concluded that highly clustered scale-free networks enhance cooperation, we find EAcluster does not perform desirably, while mlEA-CPD-SFN performs efficiently in different optimization environments. We hope that mlEA-CPD-SFN may help promote the structure of species in nature and that more general properties that enhance cooperation can be learned from the output structures.

Life and Death of Industrial Ecosystems

Self-organized industrial ecosystems (SOIEs) refer to communities of firms in diverse industries that spontaneously engage in Industrial Symbiosis (IS); that is, firms independently develop bilateral and multi-lateral interactions involving material, energy, and knowledge sharing for individual and collective benefit. Like biological ecosystems, self-organized industrial ecosystems must constantly respond to external perturbations. Resilience of SOIEs, or the ability of systems to maintain structure and function in response to perturbations, has been the focus of a few recent studies. However, these studies have only examined the network characteristics for resilience of IS in a static manner. The current study contributes to this emerging literature by examining the dynamics associated with growth (life) and demise (death) of self-organized industrial ecosystems in light of changing network dynamics and external perturbations, with emphasis on material and socio-economic aspects of connectivity between firms. This research is grounded in real world cases, but expands beyond these through hypothetical network models in order to ascertain the network characteristics that lead to more resilient structures and outcomes. A key distinction is made between SOIEs that include an anchor firm versus scavenger firms. The former typically involve a scale-free network structure where new member firms preferentially connect to actors with the most connections, while the latter involve more random, fully-connected networks where new member firms connect with multiple existing actors. The results imply that resilience of SOIEs do not arise from intrinsic properties of the system alone, but from the interplay of network topology with external social and ecological constraints.

Chinese Writing of Deaf or Hard-of-Hearing Students and Normal-Hearing Peers from Complex Network Approach.

Deaf or hard-of-hearing individuals usually face a greater challenge to learn to write than their normal-hearing counterparts. Due to the limitations of traditional research methods focusing on microscopic linguistic features, a holistic characterization of the writing linguistic features of these language users is lacking. This study attempts to fill this gap by adopting the methodology of linguistic complex networks. Two syntactic dependency networks are built in order to compare the macroscopic linguistic features of deaf or hard-of-hearing students and those of their normal-hearing peers. One is transformed from a treebank of writing produced by Chinese deaf or hard-of-hearing students, and the other from a treebank of writing produced by their Chinese normal-hearing counterparts. Two major findings are obtained through comparison of the statistical features of the two networks. On the one hand, both linguistic networks display small-world and scale-free network structures, but the network of the normal-hearing students' exhibits a more power-law-like degree distribution. Relevant network measures show significant differences between the two linguistic networks. On the other hand, deaf or hard-of-hearing students tend to have a lower language proficiency level in both syntactic and lexical aspects. The rigid use of function words and a lower vocabulary richness of the deaf or hard-of-hearing students may partially account for the observed differences.

Hypergraph partitioning for social networks based on information entropy modularity

A social network is a typical scale-free network with power-law degree distribution characteristics. It demonstrates several natural imbalanced clusters when it is abstracted as a graph, and expands quickly under its generative mechanism. Hypergraph is superior for modeling multi-user operations in social networks, and partitioning the hypergraph modeled social networks could ease the scaling problems. However, today's popular hypergraph partitioning tools are not sufficiently scalable; thus, unable to achieve high partitioning quality for naturally imbalanced datasets. Recently proposed hypergraph partitioner, hyperpart, replaces the balance constraint with an entropy constraint to achieve high-fidelity partitioning solutions, but it is not tailored for scale-free networks, like social networks. In order to achieve scalable and high quality partitioning results for hypergraph modeled social networks, we propose a partitioning method, EQHyperpart, which utilizes information-Entropy-based modularity Q value (EQ) to direct the hypergraph partitioning process. This EQ considers power-law degree distribution while describing the “natural” structure of scale-free networks. We then apply simulated annealing and introduce a new definition of hyperedge cut, micro cut, to avoid the local minima in convergence of partitioning, developing EQHyperpart into two specific partitioners, namely: EQHyperpart-SA and EQHyperpart-MC. Finally, we evaluate the utility of our proposed method using classical social network datasets, including Facebook dataset. Findings show that EQHyperpart partitioners are more scalable than competing approaches, achieving a tradeoff between modularity retaining and cut size minimizing under balance constraints, and an auto-tradeoff without balance constraints for hypergraph modeled social networks.

Analyzing and learning sparse and scale-free networks using Gaussian graphical models

In this paper, we consider the problem of fitting a sparse precision matrix to multivariate Gaussian data. The zero elements in the precision matrix correspond to conditional independencies between variables. We focus on the estimation of a class of sparse precision matrix which represents the scale-free networks. It has been demonstrated that some of the important networks display features similar to scale-free graphs. We propose a new log-likelihood formulation, which promotes the sparseness of the precision matrix as well as the topological structure of scale-free networks. To optimize this new energy formulation, the alternating direction method of multipliers form is used with the general \(L_1\)-regularized loss optimization. We tested our proposed method on various databases. Our proposed method exhibits better estimation performance with various number of samples, N, and different selection of sparsity parameter, \(\rho \).