Diffusion In Complex Networks Research Articles

On Some families of Path-related graphs with their edge metric dimension

Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models. In this paper, we study the localization problem in some path-related graphs and study the edge metric dimension. A subset LE⊆VG is known as an edge metric generator for G if, for any two distinct edges e1,e2∈E, there exists a vertex a⊆LE such that d(e1,a)≠d(e2,a). An edge metric generator that contains the minimum number of vertices is termed an edge metric basis for G, and the number of vertices in such a basis is called the edge metric dimension, denoted by dime(G). An edge metric generator with the fewest vertices is called an edge metric basis for G. The number of vertices in such a basis is the edge metric dimension, represented as dime(G). In this paper, the edge metric dimension of some path-related graphs is computed, namely, the middle graph of path M(Pn) and the splitting graph of path S(Pn).

Information cascade prediction of complex networks based on physics-informed graph convolutional network

Cascade prediction aims to estimate the popularity of information diffusion in complex networks, which is beneficial to many applications from identifying viral marketing to fake news propagation in social media, estimating the scientific impact (citations) of a new publication, and so on. How to effectively predict cascade growth size has become a significant problem. Most previous methods based on deep learning have achieved remarkable results, while concentrating on mining structural and temporal features from diffusion networks and propagation paths. Whereas, the ignorance of spread dynamic information restricts the improvement of prediction performance. In this paper, we propose a novel framework called Physics-informed graph convolutional network (PiGCN) for cascade prediction, which combines explicit features (structural and temporal features) and propagation dynamic status in learning diffusion ability of cascades. Specifically, PiGCN is an end-to-end predictor, firstly splitting a given cascade into sub-cascade graph sequence and learning local structures of each sub-cascade via graph convolutional network , then adopting multi-layer perceptron to predict the cascade growth size. Moreover, our dynamic neural network, combining PDE-like equations and a deep learning method, is designed to extract potential dynamics of cascade diffusion, which captures dynamic evolution rate both on structural and temporal changes. To evaluate the performance of our proposed PiGCN model, we have conducted extensive experiment on two well-known large-scale datasets from Sina Weibo and ArXIv subject listing HEP-PH to verify the effectiveness of our model. The results of our proposed model outperform the mainstream model, and show that dynamic features have great significance for cascade size prediction.

Random Lasers as Social Processes Simulators.

In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation in social network communities. The simulator is connected with the random laser approach that we examine in the A and D-class (superradiant) laser limits. Novel network-enforced cooperativity parameters of decision-making agents, which may be measured as a result of the solaser simulation, are introduced and justified for social systems. The innovation diffusion in complex networks is discussed as one of the possible impacts of our proposal.

Intervention against information diffusion in static and temporal coupling networks

Information diffusion in complex networks has become quite an active research topic. As an important part of this field, intervention against information diffusion processes is attracting ever-increasing attention from network and control engineers. In particular, it is urgent to design intervention schemes for the coevolutionary dynamics between information diffusion processes and coupled networks. For this purpose, we comprehensively study the problem of information diffusion intervention over static and temporal coupling networks. First, individual interactions are described by a modified activity-driven network (ADN) model. Then, we establish a novel node-based susceptible–infected–recovered–susceptible (SIRS) model to characterize the information diffusion dynamics. On these bases, three synergetic intervention strategies are formulated. Second, we derive the critical threshold of the controlled-SIRS system via stability analysis. Accordingly, we exploit a spectral optimization scheme to minimize the outbreak risk or the required budget. Third, we develop an optimal control scheme of dynamically allocating resources to minimize both system loss and intervention expense, in which the optimal intervention inputs are obtained through optimal control theory and a forward–backward sweep algorithm. Finally, extensive simulation results validate the accuracy of theoretical derivation and the performance of our proposed intervention schemes.

The interaction of multiple information on multiplex social networks

Coupled information diffusion in complex networks has been widely studied in recent years. Nevertheless, current research mainly focuses on the interaction between each information pair. In this study, we investigate the interaction of multiple types of information on multiplex networks by considering both the competition and the cooperation among them. To study the dynamic characteristics theoretically, a microscopic Markov chain approach is used to reveal the co-evolution of multiple information. Through extensive simulations, the outbreak threshold is analyzed theoretically. The results reveal that the pairwise interaction between each information pair has an obvious impact on its final outbreak scale and the diffusion threshold. Interestingly, even information that has no direct impact on the target information can affect the diffusion of the target information through indirect effects. In addition, the inhibitory effect of the competitive information and the promotion effect of the cooperative information on the target information will reach equilibrium under specific parameter space conditions. We also conduct numerical simulations on three real multiplex social networks, including two large-scale networks. Current results are beneficial for us to further understand the coupled diffusion of multiple information on multiplex social networks.

$$\text {BC}_{\mathrm {DCN}}$$: a new edge centrality measure to identify and rank critical edges pertaining to SIR diffusion in complex networks

$$\text {BC}_{\mathrm {DCN}}$$: a new edge centrality measure to identify and rank critical edges pertaining to SIR diffusion in complex networks

Effect of observation time on source identification of diffusion in complex networks

This paper examines the effect of the observation time on source identification of a discrete-time susceptible-infected-recovered diffusion process in a network with snapshot of partial nodes. We formulate the source identification problem as a maximum likelihood (ML) estimator and develop a statistical inference method based on Monte Carlo simulation (MCS) to estimate the source location and the initial time of diffusion. Experimental results in synthetic networks and real-world networks demonstrate evident impact of the observation time as well as the fraction of the observers on the concerned problem.

Computing edge version of metric and double metric dimensions of Kayak paddle graphs

Locating the source of diffusion in complex networks is an exciting but challenging task. It is critical for preventing and controlling the epidemic risks. Source localization has been studied under many feasible models. In this paper, we discuss the localization problem in Kayak paddle graphs [Formula: see text] for [Formula: see text] and [Formula: see text] by computing edge version of metric and double metric dimensions.

Coupling interaction impairs knowledge and green behavior diffusion in complex networks

Knowledge innovation, as a kind of green economic behavior, maximizes its benefits in the process of knowledge diffusion. In previous studies, the impairment or promotion of existing knowledge under different relationships on the diffusion of new knowledge and its mechanism has not been considered. On the basis of epidemic spreading model, knowledge diffusion in complex networks with interaction between two kinds of relevant knowledge is investigated in this article. Here we bridge this theoretical gap by dividing the interaction between two different kinds of knowledge into three types: interdependent, competitive and decoupled. A two-layer multiplex network is constructed to model the dynamic process. Here we assume one of the two kinds of knowledge has diffused to steady state already and pay attention to the impact from the steady knowledge on the diffusing knowledge. We derive the theoretical threshold and conduct numerical simulation of knowledge diffusion dynamic process in homogeneous network, heterogeneous network and a real citation network respectively. Theoretical results suggest that the interaction term from the steady layer is inversely proportional to the diffusion threshold in another layer. Numerical simulation shows that knowledge diffuses easier in heterogeneous networks and nodes with higher degrees. Furthermore, the final knower size of the steady knowledge impacts the diffusing knowledge positively when they are interdependent while interaction impairs both their diffusion compared with decoupled condition. According to the results, before the diffusion of innovative knowledge, the diffusion state of relevant knowledge and the influence of individual who releases innovative knowledge should be fully considered to minimize their suppression on green behavior.

Locating the Source of Diffusion in Complex Networks via Gaussian-Based Localization and Deduction

Locating the source that undergoes a diffusion-like process is a fundamental and challenging problem in complex network, which can help inhibit the outbreak of epidemics among humans, suppress the spread of rumors on the Internet, prevent cascading failures of power grids, etc. However, our ability to accurately locate the diffusion source is strictly limited by incomplete information of nodes and inevitable randomness of diffusion process. In this paper, we propose an efficient optimization approach via maximum likelihood estimation to locate the diffusion source in complex networks with limited observations. By modeling the informed times of the observers, we derive an optimal source localization solution for arbitrary trees and then extend it to general graphs via proper approximations. The numerical analyses on synthetic networks and real networks all indicate that our method is superior to several benchmark methods in terms of the average localization accuracy, high-precision localization and approximate area localization. In addition, low computational cost enables our method to be widely applied for the source localization problem in large-scale networks. We believe that our work can provide valuable insights on the interplay between information diffusion and source localization in complex networks.

How to facilitate knowledge diffusion in complex networks: The roles of network structure, knowledge role distribution and selection rule

The diffusion of knowledge within organizations provides opportunities for interpersonal co-operation, improves creative ability and therefore leads to competitive advantage. Focus of prior literature on knowledge diffusion has been on identifying factors that influence individuals' behavioral intentions to seek and share knowledge. However, knowledge diffusion as an enigmatic, emergent and organizational-level process is more than the simple aggregation of individual attributes and needs to be further investigated. Accordingly, this study focuses on three distinct system-level factors, i.e., architectures of connections among individuals, distributions of knowledge roles and designs of selection mechanisms and analyses their effects on knowledge diffusion. To be more specific, we examine three distinct knowledge roles: seekers, contributors and brokers. We also distinguish between three types of selection mechanisms: objective selection mechanisms, feedback-based selection mechanisms and random selection mechanisms. By conducting agent-based simulations on four representative networks, i.e., regular networks, random networks, small-world networks and scale-free networks, our results show that the optimal knowledge diffusion performance can be achieved on scale-free networks where all agents implement objective mechanisms and show characteristics of brokers. Moreover, our results (a) highlight the significance of brokers, (b) illustrate the superiority of objective selection rules and (c) demonstrate that scale-free networks provide an optimal framework for knowledge diffusion. Furthermore, we also find the interdependent relevance of these three factors to knowledge diffusion and propose a qualitative explanation of these findings.

Seed selection for technology innovation diffusion in complex networks

At present, the competition between enterprises is increasingly fierce. If the enterprise wants to obtain the competitive advantage, the innovation is an effective means; innovation is the basis of an enterprise’s survival and development: all enterprises strive to improve their competitiveness through innovation; however, the effects of innovation diffusion will eventually restrict their development. This study, using a complex network approach, establishes a nonlinear technology innovation diffusion cascade model aimed at identifying the best seeds to foster the process of technology innovation diffusion by searching for the important nodes scattered throughout different communities to spread technology innovation and achieve the maximum diffusion effect. Through an analysis of simulated and real networks, we found that our method can both improve the speed of technology innovation diffusion and enhance the diffusion effect, which can provide advantages to enterprises and help promote innovation.

A Method to Improve the Security of Information Diffusion in Complex Networks—Node Trust-Value Management Mechanism

The transmission of malicious information is often accompanied with normal information flows in complex networks. For the intrusion of unknown malicious information, if there is no effective defensive method to suppress its diffusion, the network may be confronted with incredible catastrophe. In this paper, to enhance the security of information diffusion in complex networks, a node trust-value management mechanism (NTVMM) is proposed. Basically, node trust value and threshold are assigned with node importance at the beginning. According to node benefit and loss in information diffusion, the two algorithms, node trust-value updated algorithm (NTVUA) and node trust-threshold updated algorithm (NTTUA), are devised to dynamically update node trust value and trust threshold, respectively. Compared with the existing node quarantine and edge blockage schemes, NTVMM only relies on the trust relationship of nodes to suppress malicious information diffusion with no need for knowing the global infection information of the network. Besides, to further make a trade-off between information security and information loss, NTVMM is associated with the classical information diffusion model to obtain the most appropriate trust threshold. Finally, we devise the network profit function to evaluate the profits brought by different methods. The simulations are respectively carried out in two synthetic complex networks and a real-world complex network. The results of simulation demonstrate that when malicious information invades the network, NTVMM can reduce the number of infected nodes in the network and enhance the security of information diffusion. Moreover, compared with node quarantine and edge blockage schemes, the proposed scheme can obtain a better network profit, and make a trade-off between information security and information loss.

Multiple propagation paths enhance locating the source of diffusion in complex networks

We investigate the problem of locating the source of diffusion in complex networks without complete knowledge of nodes’ states. Some currently known methods assume the information travels via a single, shortest path, which by assumption is the fastest way. We show that such a method leads to the overestimation of propagation time for synthetic and real networks, where multiple shortest paths as well as longer paths between vertices exist. We propose a new method of source estimation based on maximum likelihood principle, that takes into account existence multiple shortest paths. It shows up to 1.6 times higher accuracy in synthetic and real networks.

Strategic distribution of seeds to support diffusion in complex networks.

Usually, the launch of the diffusion process is triggered by a few early adopters–i.e., seeds of diffusion. Many studies have assumed that all seeds are activated once to initiate the diffusion process in social networks and therefore are focused on finding optimal ways of choosing these nodes according to a limited budget. Despite the advances in identifying influencing spreaders, the strategy of activating all seeds at the beginning might not be sufficient in accelerating and maximising the coverage of diffusion. Also, it does not capture real scenarios in which marketing campaigns continuously monitor and support the diffusion process by seeding more nodes. More recent studies investigate the possibility of activating additional seeds as the diffusion process goes forward. In this work, we further examine this approach and search for optimal ways of distributing seeds during the diffusion process according to a pre-allocated seeding budget. Theoretically, we show that a universally best solution does not exist, and we prove that finding an optimal distribution of supporting seeds over time for a particular network is an NP-hard problem. Numerically, we evaluate several seeding strategies on different networks regarding maximising the coverage and minimising the spreading time. We find that each network topology has a best strategy given some spreading parameters. Our findings can be crucial in identifying the best strategies for budget allocation in different scenarios such as marketing or political campaigns.

The effect of social tie on information diffusion in complex networks

Social network is an important carrier of information diffusion, and social tie is one of most significant factors between them. To understand the impact of social tie on information dissemination, a dynamical model with social tie strength and self-confirming mechanism is proposed and analyzed in this paper. Theoretical analysis indicates that the equilibrium of the proposed model is globally asymptotically stable, and social tie plays a key role in information propagation. Finally, some numerical simulations under synthetic networks and a partial Facebook network are given to illustrate the main results.

Effect of rich-club on diffusion in complex networks

One of the main issues in complex networks is the phenomenon of diffusion in which the goal is to find the nodes with the highest diffusing power. In diffusion, there is always a conflict between accuracy and efficiency time complexity; therefore, most of the recent studies have focused on finding new centralities to solve this problem and have offered new ones, but our approach is different. Using one of the complex networks’ features, namely the “rich-club”, its effect on diffusion in complex networks has been analyzed and it is demonstrated that in datasets which have a high rich-club, it is better to use the degree centrality for finding influential nodes because it has a linear time complexity and uses the local information; however, this rule does not apply to datasets which have a low rich-club. Next, real and artificial datasets with the high rich-club have been used in which degree centrality has been compared to famous centrality using the SIR standard.

Metapopulation dynamics and total biomass: Understanding the effects of diffusion in complex networks

In this study, I explored the impact of constructing a new dispersal route between two different patches in a metapopulation. My results indicated that its success/failure on the population abundance greatly depends on the patches directly involved and negligibly on the network topology. Specifically, constructing a dispersal route is highly recommended if it connects a source to a source that is close to becoming a sink or a sink that is close to becoming a source. This biological property is the basis for understanding the influence of the network topology on the population abundance. According to some thresholds discussed in this manuscript, I identified when a given route has a positive or negative effect on the population size. Consequently, as a simple rule of thumb, managers should look for metapopulations that have the maximum (resp. minimum) number paths with a positive (resp. negative) effect on the population abundance. As emphasized, the biological results of this paper do not depend on the model formulation.

Active influence spreading in social networks

Identifying the most influential spreaders is an important issue for the study of the dynamics of information diffusion in complex networks. In this paper we analyze the following spreading model. Initially, a few nodes know a piece of information and are active spreaders of it. At subsequent rounds, spreaders communicate the information to their neighbors. Upon receiving the information, a node becomes aware of it but does not necessarily become a spreader; it starts spreading only if it gets the information from a sufficiently large number of its neighbors. A set of initial spreaders that guarantees that all the nodes become aware of the information is called a perfect seed set. We study the problem of choosing a perfect seed set of minimum size. We provide hardness results and show that the problem becomes tractable on trees. In case of general graphs, we provide an efficient algorithm and validate its effectiveness (in terms of the solution size) on real-life networks. We also study perfect seed sets in dense graphs and derive a bound on the size of a dominating set in Ore graphs.

Knowledge diffusion in complex networks by considering time-varying information channels

In this article, based on a model of epidemic spreading, we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time-varying information channels. To cover the knowledge diffusion process in homogeneous and heterogeneous networks, two types of networks (the BA network and the ER network) are investigated. The mean-field theory is used to theoretically draw the knowledge diffusion threshold. Numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate. In addition, under the influence of the activity rate and distinct from the classic Susceptible–Infected–Susceptible (SIS) model, the density of knowers almost linearly grows with the spreading rate. Finally, in consideration of the ubiquitous mechanism of innovation, we further study the evolution of knowledge in our proposed model. The results suggest that compared with the effect of the spreading rate, the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate. Furthermore, in the BA network, the average knowledge version of individuals with higher degree is always newer than those with lower degree.