Scale-free Networks Research Articles

ATTACK VULNERABILITY OF FRACTAL SCALE-FREE NETWORK

An in-depth analysis of the attack vulnerability of fractal scale-free networks is of great significance for designing robust networks. Previous studies have mainly focused on the impact of fractal property on attack vulnerability of scale-free networks under static node attacks, while we extend the study to the cases of various types of targeted attacks, and explore the relationship between the attack vulnerability of fractal scale-free networks and the fractal dimension. A hierarchical multiplicative growth model is first proposed to generate scale-free networks with the same structural properties except for the fractal dimension. Furthermore, the fractal dimension of the network is calculated using two methods, namely, the box-covering method and the cluster-growing method, to exclude the possibility of differences in conclusions caused by the methods of calculating the fractal dimension for the subsequent relationship analysis. Finally, four attack strategies are used to attack the network, and the network performance is quantitatively measured by three structural indicators. Results on model networks show that compared to non-fractal modular networks, fractal scale-free networks are more robust to both static and dynamic targeted attacks on nodes and links, and the robustness of the network increases as the fractal dimension decreases. However, there is a cost in that as the fractal dimension decreases, the network becomes less efficient and more vulnerable to random failures on links. These findings contribute to a deeper understanding of the impact of fractal property on scale-free network performance and may be useful for designing resilient infrastructures.

Percolation in interdependent networks with groups and heterogeneous weak interdependency strength under targeted attack

Abstract Pairwise dependencies in interdependent networks exist not only between ordinary nodes but also between groups of nodes, where nodes cooperate and form groups to increase their robustness to risks and each group can be considered a ``supernode''. The interdependencies between supernodes are universal but not always complete and homogeneous. \textcolor{red}{In this paper, we study the robustness of interdependent networks with groups and heterogeneous weak interdependency strength under targeted attack, where the interdependency strength could vary between different supernodes.} We identify several types of percolation transitions, namely discontinuous, continuous, and hybrid, which are determined by the structure of the supernodes, the strengths of the interdependencies, and their distributions. We first apply this mathematical framework to the Erdös-Rényi and Scale-free interdependent networks with groups and homogeneous weak interdependency strength to calculate analytically and numerically the values of the phase transition thresholds and the critical interdependency strengths that distinguish different types of transitions. We then present examples of three distributions with different heterogeneous interdependency strengths. Our theoretical and numerical predictions are in close agreement, demonstrating that weaker interdependence strengths and higher levels of interdependence heterogeneity can enhance the robustness of interdependent networks under targeted attack.

Reflection modulation generated by scale-free network resonator periodic structure

The pattern of resonator in a periodical array is decisive for its response under impinging electromagnetic wave. A scale-free network resonator is proposed by connecting sub-units in the form of scale free network. Scale-free network resonator array’s reflectivity near resonant frequency could be modulated at arbitrary value between zero and unity, which is different from known resonator array or frequency selective surface. Reflection amplitude modulation could generate rich behaviors, as effective medium property in wide band could be maintained near zero constant, which means zero phase shift and is favorable in radar radome structure. S-parameter analysis indicates amplitude modulation is owing to polarization conversion generated by network links. Scale-free network resonator array has application potentials in future radar radomes, electromagnetic wave lens and microwave antenna panels.

The evolutionary game of emotions considering the influence of reputation

The influence of reputation and emotions on the evolution of cooperation is acknowledged, but current research predominantly focuses on one aspect. This paper integrates both reputation and emotions to examine their collective impacts on the evolution of cooperation. Initially, we define the expression of individual emotional profiles and emotional reputation. Subsequently, we consider the combined effects of the emotional reputation of an individual's neighbors and their interactive individuals on emotional responses. Further, an emotional transfer activation parameter is introduced. Lastly, we construct an algorithm for the evolutionary game of emotions. Simulation results demonstrate that considering emotional reputation is more conducive to the cooperation. The emotional reputation of interacting individuals has a greater influence on the development of positive emotions and the establishment of collaboration within groups than that of neighboring environments. In heterogeneous networks, considering the emotional reputation of neighbors increases the probability of “free-riding” by unfriendly people. When game parameters are set in favor of betrayal and negative emotions, the system evolves to produce “cautious and friendly people”. Individuals with stable emotions, high sympathy for the weak, and high respect for the strong dominate the group. Furthermore, the individuals' emotional expression towards both the weak and the strong exhibits an evolutionary synchronicity. Compared to other network structures, scale-free networks are more conducive to the evolutionary dominance of emotions of high respect for the strong.

On Low-Rank Directed Acyclic Graphs and Causal Structure Learning.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Evolution of cooperation on reinforcement-learning driven-adaptive networks.

Complex networks are widespread in real-world environments across diverse domains. Real-world networks tend to form spontaneously through interactions between individual agents. Inspired by this, we design an evolutionary game model in which agents participate in a prisoner's dilemma game (PDG) with their neighboring agents. Agents can autonomously modify their connections with neighbors using reinforcement learning to avoid unfavorable environments. Interestingly, our findings reveal some remarkable results. Exploiting reinforcement learning-based adaptive networks improves cooperation when juxtaposed with existing PDGs performed on homogeneous networks. At the same time, the network's topology evolves from homogeneous to heterogeneous states. This change occurs as players gain experience from past games and become more astute in deciding whether to join PDGs with their current neighbors or disconnect from the least profitable neighbors. Instead, they seek out more favorable environments by establishing connections with second-order neighbors with higher rewards. By calculating the degree distribution and modularity of the adaptive network in a steady state, we confirm that the adaptive network follows a power law and has a clear community structure, indicating that the adaptive network is similar to networks in the real world. Our study reports a new phenomenon in evolutionary game theory on networks. It proposes a new perspective to generate scale-free networks, which is generating scale-free networks by the evolution of homogeneous networks rather than typical ways of network growth and preferential connection. Our results provide new aspects to understanding the network structure, the emergence of cooperation, and the behavior of actors in nature and society.

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.

Goldilocks Fluctuations: Dynamic Constraints on Loop Formation in Scale-Free Transport Networks.

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behavior of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

Propagation and control of congestion risk in scale-free networks based on information entropy.

To study the propagation pattern of congestion risk in the traffic network and enhance risk control capabilities, a model has been developed. This model takes into account the probabilities of five threats (the risk occurrence probability; the risk of loss; the unpredictability of risk; the uncontrollability of risk; the transferability of risk) in the traffic network to define the risk entropy and determine the risk capacity, analyze the mechanism of congestion risk propagation, and explore the impact of risk resistance, the average degree of risk capacity at intersections, and the degree of correlation on congestion risk propagation. Further, a control method model for risk propagation is proposed. Numerical simulation results demonstrate that the risk resistance parameter θ can inhibit the propagation of congestion risk during traffic congestion. The highest efficiency in controlling risk propagation is achieved when θ reaches a threshold value θ*. Furthermore, the average degree of intersection risk capacity α shows a positive correlation with θ* and a negative correlation with control efficiency. However, the degree of association ω has a negative effect on risk propagation control, decreasing the degree of association between nodes aids in risk propagation control.

Characterization of Skeletal Muscle Regeneration Revealed a Novel Growth Network Induced by Molecular Acupuncture-like Transfection.

The low efficiency of in vivo transfection of a few fibres revealed a novel tissue network that temporally amplified growth stimulation in the entire regenerating rat soleus muscle. This acupuncture-like effect was demonstrated when the fibres began to grow after complete fibre degradation, synchronous inflammation, myoblast and myotube formation. Neonatal sarcoplasmic/endoplasmic reticulum ATPase (SERCA1b) was first detected in this system. The neonatal, fast and slow SERCA isoforms displayed consequent changes with innervation and differentiation, recapitulating events in muscle development. In vivo transfection of myotubes with plasmids expressing dominant negative Ras or a calcineurin inhibitor peptide (Cain/cabin) proved that expression of the slow myosin heavy chain and the slow muscle type SERCA2a are differentially regulated. In vivo transfection of a few nuclei of myotubes with dnRas or SERCA1b shRNA stimulated fibre size growth in the whole regenerating muscle but only until the full size had been reached. Growth stimulation by Ras and SERCA1b antisense was abolished by co-transfection of Cain or with perimuscular injection of IL4 antibody. This revealed a novel signalling network resembling scale-free networks which, starting from transfected fibre myonuclei as "hubs", can amplify growth stimulation uniformly in the entire regenerating muscle.

Complexity in road freight transport outsourcing networks. TRANSOPE: An agent-based dynamic model

This paper proposes a dynamic agent-based model (TRANSOPE) to simulate outsourcing among transport companies where, for the first time, accumulated knowledge is included as a variable to select service providers. The model consists of two main procedures. Firstly, the model simulates the decision-making of the professionals that contract transport service providers and the formation of outsourcing chains. Secondly, the model simulates the direct learning of participating companies and the transfer of knowledge towards their environment. Imperfect competition is replicated in three different scenarios, which involve the demand for transport services, regional distances and the intensity of knowledge transfer. The model is based on expert consultations and a survey conducted in an environment with a high concentration of transport companies in the Basque Country, Spain. The results indicate significant imbalances in the distribution of outsourcing, particularly in situations of low transport service demand, where 30% of transport companies do not secure any contracts. However, such situations led to strong regional interdependence. The dynamics of outsourcing reveals that over 75% of the contracted companies participate in all simulated scenarios from the first day. A strong hierarchy is also observed in the network, where certain transport companies act as connector hubs (with z-score values higher than 2.5 and participation coefficient values between 0.3 and 0.75), indicating a greater capacity for interaction and leadership in the transfer of knowledge. This feature allows the collaboration network to be identified as a scale-free network. The model has a low computational cost since the distances between agents remain constant. Finally, the formalisation of outsourcing decision-making in the model underpins its validity in forecasting the conduct of a freight transport system under shifting scenarios.

Evolution game model and simulation of enterprise R&D cooperative innovation network under network externalities

ABSTRACT Multi-agent cooperation, pooling innovative resources, helps to develop key technologies and major projects in enterprises. However, the multi-agent cooperation of enterprises makes the cooperative relationship unstable, and behaviours such as moral hazard, spillover of technology or information are more likely to occur, thereby increasing the risk of enterprises. In this research an enterprise R&D cooperative evolutionary game model is built to investigate the influence of Network externalities on enterprise R&D cooperation in innovation networks. Furthermore, the evolution of innovative network structure of game results is simulated by means of computer technology so that the effects of network externalities on corporation degree, agglomeration and network structure are analyzed. The results show that Network externalities led to a decrease of cooperated partners, a decline in cooperation degree and agglomeration of enterprises, and a shrinking enterprise R&D cooperation tendency. The influence of network externalities shows significant structural differences in the three types of enterprise networks: the degree of enterprise cooperation and agglomeration fluctuates greatly in the scale-free network, but slightly in the small-world network and the random network.

Hyperbolic multichannel graph convolutional network for social recommendation

Social recommendations enhance the quality of recommendations by integrating social network information. Existing methods predominantly rely on pairwise relationships to uncover potential user preferences. However, they usually overlook the exploration of higher-order user relations. Moreover, because social relation graphs often exhibit scale-free graph structures, directly embedding them in Euclidean space will lead to significant distortion. To this end, we propose a novel graph neural network framework with hypergraph and hyperbolic embedding learning, namely HMGCN. Specifically, we first construct hypergraphs over user-item interactions and social networks, and then perform graph convolution on the hypergraphs. At the same time, a multi-channel setting is employed in the convolutional network, with each channel encoding its corresponding hypergraph to capture different high-order user relation patterns. In addition, we feed the item embeddings and the obtained high-order user embeddings into a hyperbolic graph convolutional network to extract user and item representations, enabling the model to better capture the hierarchical structure of their complex relationships. Experimental results on three public datasets, namely FilmTrust, LastFM, and Yelp, demonstrate that the model achieves more comprehensive user and item representations, more accurate fitting and processing of graph data, and effectively addresses the issues of insufficient user relationship extraction and data embedding distortion in social recommendation models.

Synchronization in scale-free neural networks under electromagnetic radiation.

The functional networks of the human brain exhibit the structural characteristics of a scale-free topology, and these neural networks are exposed to the electromagnetic environment. In this paper, we consider the effects of magnetic induction on synchronous activity in biological neural networks, and the magnetic effect is evaluated by the four-stable discrete memristor. Based on Rulkov neurons, a scale-free neural network model is established. Using the initial value and the strength of magnetic induction as control variables, numerical simulations are carried out. The research reveals that the scale-free neural network exhibits multiple coexisting behaviors, including resting state, period-1 bursting synchronization, asynchrony, and chimera states, which are dependent on the different initial values of the multi-stable discrete memristor. In addition, we observe that the strength of magnetic induction can either enhance or weaken the synchronization in the scale-free neural network when the parameters of Rulkov neurons in the network vary. This investigation is of significant importance in understanding the adaptability of organisms to their environment.

Granting leaders priority exit options promotes and jeopardizes cooperation in social dilemmas

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner’s dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts.

Quantum transport on multilayer generalized scale-free networks

Abstract We study single-particle quantum transport on multilayer generalized scale-free networks using the continuous-time quantum walk model. Our focus is directed at the average return probability and its long-time average value as measures for the transport efficiency. In the continuous-time model these quantities are completely determined by all the eigenvalues and eigenvectors of the connectivity matrix. For all multilayer networks a nontrivial interplay between good spreading and localization effects is observed. The spreading is enhanced by increasing the number of layers L or the power-law exponent γ of the degree distribution. For our choice of the parameters, namely L (1 ≤ L ≤ 50) or γ (1 ≤ γ ≤ 4), the quantum efficiency is increased by at least one order of magnitude. The topological transition between networks without loops, which corresponds to a single scale-free network layer (L = 1), and networks with loops (L = 2) is the most impactful. Another important change occurs when L gets higher than the average diameter d of the layers, namely a new scaling behavior for random walks and lower fluctuations around the long-time average value for quantum walks. The quantum transport is more sensitive to changes of the minimum allowed degree, K min, than to the maximum allowed degree, K max. The same quantum efficiency is found by varying at least one of the parameters: L, γ, K min, or K max, although the network’s topology is different. The quantum efficiency of all multilayer scale-free networks shows a universal behavior for any size of the layers, more precise, is inversely proportional to the number of layers.

Understanding route choice behaviors' impact on traffic throughput in a dynamic transportation network

Route planning is one of the most important and attractive topics in complex networks, geographical information science (GIS) and logistics. Travelers' route choice behaviors may affect the actual throughput of a transportation network. This study aims to analyze the influence of travelers' route choice behaviors on network traffic throughput. Two kinds of route choice behaviors, called continuous optimization behavior and hybrid optimization behavior, are defined. Based on this, two traffic scenarios are constructed to describe these behaviors and examine their effect on the network's actual traffic throughput. The application of our approach to urban street networks, Barabási-Albert scale-free network and Erdös-Rényi random network demonstrates that if all travelers choose optimal paths constraint with time from the start, network throughput is insensitive to the continuous optimization behavior but depends on the relationship between time and distance in the routing algorithm. Besides, network throughput is sensitive to the hybrid optimization behavior that the more travelers choose time-dependent optimal paths, the higher the throughput. The results indicate that the choice of initial paths and the time dependence of routing algorithms can directly affect the network's actual throughput which is enhanced >50 % when the time dependence parameter is >0.2 or the proportion of time-dependent shortest paths in initial paths is >0.2. Our findings provide supports for exploring efficient routing algorithms to enhance the throughput of urban street networks and other kinds of networks.

Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena

By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software can be applied to any kind of network and “target” correlations, but it is tested with focus on scale-free networks and assortative correlations. In order to generate the degree sequence we use the method of “random hubs”, which gives networks with minimal fluctuations. For the assortative rewiring we use the simple Vazquez-Weigt matrix as a test in the case of random networks; since it does not appear to be effective in the case of scale-free networks, we subsequently turn to another recipe which generates matrices with decreasing off-diagonal elements. The rewiring procedure is also important at the theoretical level, in order to test which types of statistically acceptable correlations can actually be realized in concrete networks. From the point of view of applications, its main use is in the construction of correlated networks for the solution of dynamical or diffusion processes through an analysis of the evolution of single nodes, i.e., beyond the Heterogeneous Mean Field approximation. As an example, we report on an application to the Bass diffusion model, with calculations of the time tmax of the diffusion peak. The same networks can additionally be exported in environments for agent-based simulations like NetLogo.

Identifying risks in temporal supernetworks: an IO-SuperPageRank algorithm

Complex systems pose risks characterized by factors such as uncertainty, nonlinearity, and diversity, making traditional risk measurement methods based on a probabilistic framework inadequate. Supernetworks can effectively model complex systems, and temporal supernetworks can capture the dynamic evolution of these systems. From the perspective of network stability, supernetworks can aid in risk identification for complex systems. In this paper, an IO-SuperPageRank algorithm is proposed based on the supernetwork topological structure. This algorithm reveals network instability by calculating changes in node importance, thereby helping to identify risks in complex systems. To validate the effectiveness of this algorithm, a four-layer supernetwork composed of scale-free networks is constructed. Simulated experiments are conducted to assess the impact of changes in intralayer edge numbers, intralayer node numbers, and interlayer superedge numbers on the risk indicator IO value. Linear regression and multiple tests were used to validate these relationships. The experiments show that changes in the three network topological indicators all bring about risks, with changes in intralayer node numbers having the most significant correlation with the risk indicator IO value. Compared to traditional measures of network node centrality and connectivity, this algorithm can more accurately predict the impact of node updates on network stability. Additionally, this paper collected trade data for crude oil, chemical light oil, man-made filaments and man-made staple fibers from the UN Comtrade Database. We constructed a man-made filaments and fibers supply chain temporal supernetwork, utilizing the algorithm to identify supply chain risks from December 2020 to October 2023. The study revealed that the algorithm effectively identified risks brought about by changes in international situations such as the Russia-Ukraine war, Israel–Hamas conflict, and the COVID-19 pandemic. This demonstrated the algorithm’s effectiveness in empirical analysis. In the future, we plan to further expand its application based on different scenarios, assess risks by analyzing changes in specific system elements, and implement effective risk intervention measures.

Interplay of network topologies in aviation delay propagation: A complex network and machine learning analysis

In this study, the fundamental characteristics of flight delay propagation and the key factors influencing such propagation are investigated. Three distinct types of networks were constructed: an aviation network, a traffic flow network, and a delay propagation network. Employing complex network theory, an analysis of the fundamental topological attributes of each network was conducted, exploring the interrelations among these attributes. Findings reveal a notable resemblance between the network topology attributes of the delay propagation network and the traffic flow network. The delay propagation network overall adheres to scale-free network attributes, with a few dominant major airports playing a pivotal role in the delay propagation process. Furthermore, it was uncovered that smaller airports are more susceptible to the influence of delay propagation than their larger counterparts. Delays, in a general sense, exhibit a pronounced tendency to aggregate and spread extensively within the realm of smaller airports. Regarding delay propagation, airport traffic emerges as the primary factor precipitating this phenomenon, with a feature importance score reaching 0.889. An escalation in airport traffic significantly amplifies the extent of delay propagation, yet concurrently, this escalation is not incessant but stabilizes beyond a certain threshold.