Random Regular Networks Research Articles

Reference to Global State and Social Contagion Dynamics

The network-based model of social contagion has revolved around information on local interactions; its central focus has been on network topological properties shaping the local interactions and, ultimately, social contagion outcomes. We extend this approach by introducing information on the global state, or global information, into the network-based model and analyzing how it alters social contagion dynamics in six different classes of networks: a two-dimensional square lattice, small-world networks, Erdős-Rényi networks, regular random networks, Holme-Kim networks, and Barabási-Albert networks. We find that there is an optimal amount of global information that minimizes the time to reach global cascades in highly clustered networks. We also find that global information prolongs the time to hit the tipping point but substantially compresses the time to reach global cascades after then, so that the overall time to reach global cascades can even be shortened under certain conditions. Finally, we show that random links substitute for global information in regulating the social contagion dynamics.

Nanostructure regularity in white beetle scales for stability and strong optical scattering [Invited

Cyphochilus white beetle scales exhibit exceptionally strong light scattering power that originates from their regular random fibrillar network nanostructure. The structure is believed to be formed by late-stage spinodal decomposition in a lipid membrane system. However, the structure is characterized by nonconstant mean curvatures and appreciable anisotropy, which are not expected from late-stage spinodal decomposition, so that the surface free energy is not minimized. Nevertheless, a high degree of regularity represented by the relatively uniform fibril dimensions and smooth fibril surfaces in the structure may result from a process similar to spinodal decomposition. In this study, we investigate the role of regularity in the Cyphochilus white beetle scale structure in realizing strong light scattering. Irregularity is computationally introduced into the structure in a systematic fashion such that its anisotropy is preserved and its surface area is kept constant. Calculations show that optical scattering power decreases as irregularity increases with a high sensitivity. This effect happens because, remarkably, irregularity on a scale much smaller than the wavelength destroys anisotropy in optical diffusion. Thus, the result shows that the in vivo process in Cyphochilus white beetle scales utilizes structural regularity and anisotropy to achieve strong light scattering at a tolerable surface free energy. In typical fabrication of random media, irregularity and multiple length scales typically increase surface area, so that durability of the nanostructures may be negatively affected. Our study indicates that regularity in anisotropic random nanostructures can achieve strong light scattering with a moderate surface free energy.

Quantum Contagion: A Quantum-Like Approach for the Analysis of Social Contagion Dynamics with Heterogeneous Adoption Thresholds.

Modeling the information of social contagion processes has recently attracted a substantial amount of interest from researchers due to its wide applicability in network science, multi-agent-systems, information science, and marketing. Unlike in biological spreading, the existence of a reinforcement effect in social contagion necessitates considering the complexity of individuals in the systems. Although many studies acknowledged the heterogeneity of the individuals in their adoption of information, there are no studies that take into account the individuals’ uncertainty during their adoption decision-making. This resulted in less than optimal modeling of social contagion dynamics in the existence of phase transition in the final adoption size versus transmission probability. We employed the Inverse Born Problem (IBP) to represent probabilistic entities as complex probability amplitudes in edge-based compartmental theory, and demonstrated that our novel approach performs better in the prediction of social contagion dynamics through extensive simulations on random regular networks.

Social percolation revisited: From 2d lattices to adaptive networks

The social percolation model Solomon et al. (2000) considers a 2-dimensional regular lattice. Each site is occupied by an agent with a preference xi sampled from a uniform distribution U[0,1]. Agents transfer the information about the quality q of a movie to their neighbors only if xi≤q. Information percolates through the lattice if q=qc=0.593. – From a network perspective the percolating cluster can be seen as a random–regular network with nc nodes and a mean degree that depends on qc. Preserving these quantities of the random–regular network, a true random network can be generated from the G(n,p) model after determining the link probability p. I then demonstrate how this random network can be transformed into a threshold network, where agents create links dependent on their xi values. Assuming a dynamics of the xi and a mechanism of group formation, I further extend the model toward an adaptive social network model.

Regulating lithium deposition via bifunctional regular-random cross-linking network solid polymer electrolyte for Li metal batteries

The low coulombic efficiency and poor cycle performance deriving from uncontrolled growth of dendrites have caused a serious obstacle to the practical application of lithium metal. Herein we propose a bifunctional regular-random dual cross-linking network solid polymer electrolyte (RRa-SPE) for dendrite-free all-solid-state lithium metal batteries. Under the synergistic effect of regular polymerization skeleton and random cross-linking network, the RRa-SPE effectively regulates the lithium deposition and facilitates the generation of a highly homogeneous and robust solid-electrolyte interphase (SEI) layer on lithium metal. Besides, this RRa-SPE shows benign ionic conductivity of 4.36 × 10−4 S cm−1 (at 30 °C), high lithium ion transference number of 0.76 and enhanced mechanical strength. The Li/RRa-SPE/Li symmetric cell maintains low and stable voltage polarization (0.15 V) after circulating for 1200 h at 0.5 mA cm−2. Improved LiFePO4/RRa-SPE/Li cell exhibits excellent rate capability and prominent cycle performance with a capacity retention of 99.6% after 240 cycles at 0.5 C at 30 °C.

SEAIR Epidemic spreading model of COVID-19.

We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all three versions, which hold when the epidemic is weak. We provide theoretical arguments that eigenvector centrality of a node approximately determines its risk to become infected.

Toward a more Efficient Knowledge Network in Innovation Ecosystems: A Simulated Study on Knowledge Management

Knowledge management has become increasingly important in the era of knowledge economy. This study explores what is an optimal knowledge network for more efficient knowledge diffusion among strategic partners in order to provide insights on sustainable enterprises and a more knowledge-efficient innovation ecosystem. Based on simulated analyses of the efficiency of knowledge network models, including regular network, random network, and small world network, this study shows that a random knowledge network is more efficient for knowledge diffusion when a mixture knowledge trade rule is used. This study thus helps identify which knowledge networks facilitate knowledge exchange among collaborative partners for sustainable knowledge management. Management practitioners and policymakers can use the findings to design more appropriate knowledge exchange networks to improve the efficiency of knowledge diffusion in an innovation ecosystem.

Algorithms for tensor network contraction ordering

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. Furthermore, we present a systematic comparison with state-of-the-art tree decomposition and graph partitioning algorithms in the context of random regular graph tensor networks. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.

Diffusion of innovations in finite networks: Effects of heterogeneity, clustering, and bilingual option on the threshold in the contagion game model

The contagion threshold for diffusion of innovations is defined and calculated in finite graphs (two-dimensional regular lattices, regular random networks (RRNs), and two kinds of scale-free networks (SFNs)) with and without the bilingual option. Without the bilingual option, degree inhomogeneity and clustering enhance the contagion threshold in non-regular networks except for those with an unrealistically small average degree. It is explained by the friendship paradox and detour effect. We found the general boundary of the cost that makes the bilingual option effective. With a low-cost bilingual option, among regular lattices, SFNs, and RRNs, the contagion threshold is largest in regular lattices and smallest in RRNs. The contagion threshold of regular random networks is almost the same as that of the regular trees, which is the minimum among regular networks. We show that the contagion threshold increases by clustering with a low-cost bilingual option.

Estimating the Information Source under Decaying Diffusion Rates

Recently, as arising from online social network services such as Facebook and Twitter, people are more actively using social networks to exchange their new information. In this consideration, finding the information source becomes one of the indispensable and useful tasks in detecting a malicious agent and an influential person in the networks. A seminal work by Shah and Zaman in 2010 showed that the detection probability cannot be beyond 31% even for regular trees if time goes to infinity. From the study, extensive researches have been done for this problem, whose major interests lie in constructing an efficient estimator and providing theoretical analysis on its detection performance. However, most of the works assumed the homogeneous diffusion rate of the information, where the diffusion rate does not change at all times over the network. In practice, it is reported that information has a lifetime and it becomes less attractive over time. In this paper, we study the problem of detecting the information source when the diffusion rate decreases by the distance from the source in the network. As a result, we obtain analytical detection performance of Maximum Likelihood Estimator (MLE) and validate our theoretical findings over the regular tree, random and real-world networks.

Dynamical correlations and pairwise theory for the symbiotic contact process on networks.

The two-species symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.

Highly clustered complex networks in the configuration model: Random regular small-world network

We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed their properties. We show that highly clustered random regular networks with appropriate parameters satisfy all the conditions of the small-world network: connectedness, high clustering coefficient, and small-world effect. We also study how clustering affects the percolation threshold in random regular networks. In addition, the prisoner's dilemma game is studied and the effects of clustering and degree heterogeneity on the cooperation level are discussed.

Eradicating abrupt collapse on single network with dependency groups.

The dependency among nodes has significant effects on the cascading failures of complex networks. Although the prevention of cascading failures on multilayered networks in which the failures of nodes in one layer affect the functioning of nodes in other layers has been widely investigated, the prevention of catastrophic cascade has rarely been addressed to single-layer networks where nodes are grouped and nodes within the same group are dependent on each other. For such networks, we find that it is already enough to prevent abrupt catastrophic collapses by randomly reinforcing a constant density of nodes. More importantly, we give the analytical solutions to the proportion of needed reinforced nodes for three typical networks, i.e., dependent Erdős-Rényi (ER), random regular (RR), and scale-free (SF) networks. Interestingly, the density of reinforced nodes is a constant 0.1756, which holds true for ER networks with group size 2 regardless of average degree, RR, and SF networks with a large average degree. Also, we find the elegant expression of the density with any group size. In addition, we find a hybrid phase transition behavior, which is present in RR and SF networks while absent in ER networks. Our findings might shed some new light on designing more resilient infrastructure networks.

Synchronization for discrete-time complex networks with probabilistic time delays

This paper investigates the problem of adaptive synchronization for discrete-time complex dynamical networks with random delays. In such complex systems, there occurs two kinds of nonidentical probability delays, i.e. self-feedback delays and coupling delays, and these delays are assumed to take values in a given finite sets with probability distributions. By means of the Lyapunov theory, discrete-time Jensen inequality and reciprocal convex combination approach, several delay-probability-distribution-dependent conditions are derived in the linear matrix inequality (LMI) format such that the discrete-time complex dynamical networks with random delays are globally synchronization in mean square. In addition, we use Watts–Strogatz (WS) random complex networks and regular Rulkov networks as two numerical examples to illustrate the effectiveness of our theoretical analysis.

Distinct dynamical behavior in Erdős-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks.

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdős-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. While ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely, ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.

Parent-preferred dispersal promotes cooperation in structured populations.

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth-death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

Multiple phase transitions in networks of directed networks

The robustness in real-world complex systems with dependency connectivities differs from that in isolated networks. Although most complex network research has focused on interdependent undirected systems, many real-world networks-such as gene regulatory networks and traffic networks-are directed. We thus develop an analytical framework for examining the robustness of networks made up of directed networks of differing topologies. We use it to predict the phase transitions that occur during node failures and to generate the phase diagrams of a number of different systems, including treelike and random regular (RR) networks of directed Erdős-Rényi (ER) networks and scale-free networks. We find that the the phase transition and phase diagram of networks of directed networks differ from those of networks of undirected networks. For example, the RR networks of directed ER networks show a hybrid phase transition that does not occur in networks of undirected ER networks. In addition, system robustness is affected by network topology in networks of directed networks. As coupling strength q increases, treelike networks of directed ER networks change from a second-order phase transition to a first-order phase transition, and RR networks of directed ER networks change from a second-order phase transition to a hybrid phase transition, then to a first-order phase transition, and finally to a region of collapse. We also find that heterogenous network systems are more robust than homogeneous network systems. We note that there are multiple phase transitions and triple points in the phase diagram of RR networks of directed networks and this helps us understand how to increase network robustness when designing interdependent infrastructure systems.

Localized attack on networks with clustering

Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős–Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value qc. Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q < qc, the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA.

Percolation on random networks with proliferation

The literature on growing network models, exemplified by the preferential attachment model and the copying model, has followed an exponential growth in the last few years. In many real-life scenarios, however, the adding of new nodes and edges is not an exogenous process, but involves inheritance and sharing of the local environment of the existing ones. In this paper, we develop a mathematical framework to analytically and numerically study the percolation properties of the random networks with proliferation. We compare random attack (RA) and localized attack (LA) on benchmark models, including Erdős–Rényi (ER) networks, random regular (RR) networks, and scale-free (SF) networks, with proliferation mechanism. Our results highlight the nonmonotonic connections with robustness and growth, and unravel an intriguing opposite effect for RA and LA. In particular, it is shown that unbalanced proliferation enhances robustness to RA while it mitigates robustness to LA, both independent of the network degree distribution.

Social contagions with communication channel alternation on multiplex networks

Internet communication channels, e.g., Facebook, Twitter, and email, are multiplex networks that facilitate interaction and information-sharing among individuals. During brief time periods users often use a single communication channel, but then communication channel alteration (CCA) occurs. This means that we must refine our understanding of the dynamics of social contagions. We propose a non-Markovian behavior spreading model in multiplex networks that takes into account the CCA mechanism, and we develop a generalized edge-based compartmental method to describe the spreading dynamics. Through extensive numerical simulations and theoretical analyses we find that the time delays induced by CCA slow the behavior spreading but do not affect the final adoption size. We also find that the CCA suppresses behavior spreading. On two coupled random regular networks, the adoption size exhibits hybrid growth, i.e., it grows first continuously and then discontinuously with the information transmission probability. CCA in ER-SF multiplex networks in which two subnetworks are Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) introduces a crossover from continuous to hybrid growth in adoption size versus information transmission probability. Our results extend our understanding of the role of CCA in spreading dynamics, and may elicit further research.