Erdos-Renyi Research Articles

The impact of social noise on the majority rule model across various network topologies

We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order–disorder transition can reflect the consensus-polarization state in a social context. This study covers various network topologies, including complete graphs, two-dimensional (2-D) square lattices, three-dimensional (3-D) square lattices, and heterogeneous or complex networks such as Watts–Strogatz (W-S), Barabási-Albert (B-A), and Erdős-Rényi (E-R) networks, as well as their combinations (multilayer network). Social behavior is represented by the parameter p, which indicates the probability of agents exhibiting nonconformist behavior. Our results show that the model exhibits a continuous phase transition across all networks. Through finite-size scaling analysis and evaluation of critical exponents, our results suggest that the model falls into the same universality class as the Ising model.

Scaling behavior of cross-entropy loss in the identification of percolation phase transitions.

The cross-entropy loss function is widely used in machine learning to measure the performance of a classification model. Interestingly, our study find that this function has scaling behavior when deep neural networks are used to investigate percolation models. Specifically, we use convolutional neural networks with different pooling methods to study the site percolation on square lattices under two labeling methods (labeling based on spanning cluster and the exact solution of the critical point). Subsequently, graph convolutional neural networks (GCNs) with different pooling methods are utilized to do the same kind of experiment. Finally, the GCN with different pooling methods is used to study the percolation phase transitions on the Erdős-Rényi (ER) networks under labeling based on the critical point. The reliability of the classifiers is detected by the values of the critical point p_{c} and critical exponent ν which are obtained by the scaling behaviors of the percolation probability. The results demonstrate that the scaling exponent of cross-entropy ψ/ν depends on the labeling and pooling methods. Labeling based on critical points, which is equivalent to labeling based on spanning clusters in infinite systems, can be used to investigate the critical behaviors in finite systems. SAGPooling-Mean is an effective pooling method to study the scaling behavior of cross-entropy loss on two-dimensional square lattices and ER networks.

The adaptive consensus reaching process with the ER-PSO interaction mechanism and its application in public charging stations evaluation

BackgroundPublic charging stations (PCSs) have become integral public infrastructure in China, responding to the considerable and rapidly growing demand. Evaluating the service quality of PCSs by a diverse user base has become essential for the effective management of PCSs. ObjectivesIn the group evaluation of PCSs' service quality, which encompasses broad public interests, consensus reaching process (CRP) is commonly utilized to manage group conflicts and achieve evaluation consensus. The intricate interactions among decision makers (DMs) significantly influence the evolution and resilience of collective viewpoints. Against this backdrop, this research aims to develop an adaptive CRP to enhance the discriminatory power of group consensus and improve consensus robustness in the presence of non-cooperative behavior. MethodologyWith the above objectives, this study proposes an adaptive CRP supported by a novel interaction mechanism, consisting of two stages: (1) In the interaction network generation stage, based on the Erdős-Rényi (ER) random network model, innovative interaction signals are generated to guide the generation of an ER-based interaction network, enhancing the dissemination of dominant viewpoints, and constraining the influence of minority opinions. (2) In the decision opinion interaction stage, based on the Particle Swarm Optimization (PSO) algorithm, utilizing novel dual individual fitness functions, the PSO algorithm is employed to formulate the expected updated belief, driving the internal evolution and convergence of opinions. The proposed adaptive CRP is implemented in the group evaluation of PCSs' service quality in Nanjing. FindingsComparative analysis reveals that the proposed CRP offers significant advantages in consensus efficiency, the discriminatory power of group consensus, and consensus robustness in the presence of non-cooperative behavior compared to existing CRPs. NoveltyDiffering from previous CRP research primarily focuses on minimizing adjustment scales, this study emphasizes the adaptive evolution and convergence of opinions, providing a more suitable description of group opinion dynamics. Additionally, from a methodological perspective, this research utilizes the ER network model and the PSO algorithm to support the adaptive CRP at both structural and preference levels, enhancing consensus discriminatory power and robustness.

The impact of conditional coupling based on environment comparison between interdependent networks on the evolution of cooperation

The coupling between interdependent networks is a crucial factor affecting the evolution of cooperation. Actually, not all nodes in different sub-networks of the interdependent network can establish a one-to-one corresponding coupling relationship, and whether the connection between corresponding nodes can be built is often related to the local environment and global environment where the individual is located. Therefore, we explore how the conditional coupling between interdependent networks based on the comparisons of local and global environments affects the spread of cooperative behavior. We consider two types of conditional coupling modes: static coupling and dynamic coupling. The classic prisoner’s dilemma is chosen as the fundamental game model. The numerical simulation results on the interdependent network constructed by square lattices show that conditional coupling based on environmental comparison favors the propagation of cooperation, regardless of the type of conditional coupling. And the promotion level of cooperation is proportional to the coupling strength. Moreover, we further perform the simulation experiments on the interdependent networks composed of ER (Erdös–Rényi) random networks. Our explorations may be helpful for understanding the survival and maintenance of cooperation in the interconnected and interrelated systems.

Percolation of conditional dependency clusters based on edge-coupled interdependent networks

Considering the existence of multiple edge dependencies in realistic interdependent networks, we propose a model of edge-coupled interdependent networks with conditional dependency clusters (EINCDCs). In this model, the edges in network A depend on the edges in dependency clusters of size m in network B. If the failure rate of edges within the dependency clusters in network B exceeds the failure tolerance α, the corresponding edges in network A that depend on those clusters in network B will fail accordingly. By adopting the self-consistent probabilities approach, a theoretical analytical framework is established to quantitatively address this model. Specifically, we study the robustness of the system verified with numerical simulations in the effect of the cluster size and failure tolerance under random attacks on systems composed of two networks A and B constructed with Random Regular (RR), Erdös-Rényi (ER) and Scale Free (SF) models. Our results show that both networks A and B undergo a first-order or hybrid phase transition when the dependency cluster size does not exceed 2. However, when the cluster size of dependency clusters exceeds 2, a non-monotonic behavior is observed. In particular, when the failure tolerance is in the range from 0 to 0.5, the robustness of the system weakens with the growing in the number of dependency clusters of size 2. While, this tendency reverses when the failure tolerance is in the range from 0.5 to 1. Moreover, we observe that due to the asymmetric interdependency between the two networks, network B always undergoes first-order phase transition, whereas network A could exhibit different types of phase transitions, which depends on the size of dependency clusters. In addition, the failure tolerance may have opposite effects on the two networks with the growing of dependency cluster sizes. The conclusions of the study may provide useful implications and enrich the understanding in the robustness of edge-coupled interdependent networks.

Node and edge centrality based failures in multi-layer complex networks

Multi-layer complex networks (MLCN) appears in various domains, such as, transportation, supply chains, etc. Failures in MLCN can lead to major disruptions in systems. Several research have focussed on different kinds of failures, such as, cascades, their reasons and ways to avoid them. This paper considers failures in a specific type of MLCN where the lower layer provides services to the higher layer without cross layer interaction, typical of a computer network. A three layer MLCN is constructed with the same set of nodes where each layer has different characteristics, the bottom most layer is Erdos–Renyi (ER) random graph with shortest path hop count among the nodes as gaussian, the middle layer is ER graph with higher number of edges from the previous, and the top most layer is preferential attachment graph with even higher number of edges. Both edge and node failures are considered. Failures happen with decreasing order of centralities of edges and nodes in static batch mode and when the centralities change dynamically with progressive failures. Emergent pattern of three key parameters, namely, average shortest path length (ASPL), total shortest path count (TSPC) and total number of edges (TNE) for all the three layers after node or edge failures are studied. Extensive simulations show that all but one parameters show definite degrading patterns. Surprising, ASPL for the middle layer starts showing a chaotic behaviour beyond a certain point for all types of failures.

Discovering the signal subgraph: An iterative screening approach on graphs

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.

Topological and spectral properties of random digraphs.

We investigate some topological and spectral properties of Erdős-Rényi (ER) random digraphs of size n and connection probability p,D(n,p). In terms of topological properties, our primary focus lies in analyzing the number of nonisolated vertices V_{x}(D) as well as two vertex-degree-based topological indices: the Randić index R(D) and sum-connectivity index χ(D). First, by performing a scaling analysis, we show that the average degree 〈k〉 serves as a scaling parameter for the average values of V_{x}(D),R(D), and χ(D). Then, we also state expressions relating the number of arcs, largest eigenvalue, and closed walks of length 2 to (n,p), the parameters of ER random digraphs. Concerning spectral properties, we observe that the eigenvalue distribution converges to a circle of radius sqrt[np(1-p)]. Subsequently, we compute six different invariants related to the eigenvalues of D(n,p) and observe that these quantities also scale with sqrt[np(1-p)]. Additionally, we reformulate a set of bounds previously reported in the literature for these invariants as a function (n,p). Finally, we phenomenologically state relations between invariants that allow us to extend previously known bounds.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

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.

Hybrid cascade failures in supply chain networks: Robustness, node protection and recovery strategies

This study investigates the influence of mixed cascade failures on the resilience of manufacturing enterprise supply chain networks, which are susceptible to disruptions from upstream and downstream enterprises due to external uncertainties. We propose a single-layer directed network model to examine mixed cascade failures and analyze the effectiveness of protection and recovery strategies for improving network resilience through extensive simulation experiments. The numerical analysis yields the following key findings: (i) Under targeted attacks, the Erdős–Rényi (ER) network exhibits marginally enhanced robustness, whereas the Barabási–Albert (BA) network proves to be more resilient against random attacks. (ii) Effectively mitigating failure risk and reducing the likelihood of failure can be accomplished by increasing the upper load capacity limit and decreasing the lower load capacity limit for manufacturing firms. Furthermore, a comprehensive approach to protection and recovery measures strengthens the stability of supply chain networks in the face of external risks. (iii) Constraints, such as epidemic control measures and infrastructure damage, may impede the recovery process of manufacturing firms’ supply chains when addressing external uncertainties.

Large-scale robustness-oriented efficient edge addition through traversal tree-based weak edge identification

To build robust networks, a popular way is to add edges to existing networks, which can help defend against natural disasters or malicious attacks that randomly or intentionally break several key links at once. There is an urgent need to optimally add edges to improve robustness, e.g., measured by general metrics such as graph connectivity. However, although exhausting and connecting both sides of all small cuts is a sure way to achieve feasible solutions, since the number of possible edges to add is much more than the existing number of edges, even the problem instances in the small graphs are too complex to be solved efficiently, while applying heuristic algorithms to large-scale graphs can only achieve very inefficient results. Fortunately, we find an efficient way to represent all candidate cuts based on the mapping between trees and cuts, and find the near-optimal set of endpoints that cross both sides of all these cuts, and finally find the optimal number of edges reinforcing these cuts to improve edge connectivity. Experiments in representative Erdos–Renyi and scale-free graphs show that the proposed algorithm can achieve perfectly improved results as the optimal algorithm, and the computing speed can be at most 6 orders of magnitude faster than the optimal algorithm, at the expense of slightly increased edge count. The large graph results show the obvious advantage of the proposed algorithms in providing near-perfect results, while popular heuristic algorithms are almost useless in protecting these networks. The proposed algorithm can be further efficient by exploiting its ready-to-parallelize logics for further acceleration.

‘I don’t want to play with you anymore’: dynamic partner judgements in moody reinforcement learners playing the prisoner’s dilemma

Abstract Emerging reinforcement learning algorithms that utilize human traits as part of their conceptual architecture have been demonstrated to encourage cooperation in social dilemmas when compared to their unaltered origins. In particular, the addition of a mood mechanism facilitates more cooperative behaviour in multi-agent iterated prisoner dilemma (IPD) games, for both static and dynamic network contexts. Mood-altered agents also exhibit humanlike behavioural trends when environmental aspects of the dilemma are altered, such as the structure of the payoff matrix used. It is possible that other environmental effects from both human and agent-based research will interact with moody structures in previously unstudied ways. As the literature on these interactions is currently small, we seek to expand on previous research by introducing two more environmental dimensions; voluntary interaction in dynamic networks, and stability of interaction through varied network restructuring. From an initial Erdos–Renyi random network, we manipulate the structure of a network IPD according to existing methodology in human-based research, to investigate possible replication of their findings. We also facilitated strategic selection of opponents through the introduction of two partner evaluation mechanisms and tested two selection thresholds for each. We found that even minimally strategic play termination in dynamic networks is enough to enhance cooperation above a static level, though the thresholds for these strategic decisions are critical to desired outcomes. More forgiving thresholds lead to better maintenance of cooperation between kinder strategies than stricter ones, despite overall cooperation levels being relatively low. Additionally, moody reinforcement learning combined with certain play termination decision strategies can mimic trends in human cooperation affected by structural changes to the IPD played on dynamic networks—as can kind and simplistic strategies such as Tit-For-Tat. Implications of this in comparison with human data is discussed, and suggestions for diversification of further testing are made.

A two-layer model with partial mapping: Unveiling the interplay between information dissemination and disease diffusion

This study delves into the pivotal role of information dissemination in public health, particularly how it influences the spread of diseases. By implementing a sophisticated two-layer partial mapping network model (UAU-SIRS), we investigate the dynamic relationship between information flow and disease transmission. Our approach utilizes extensive multiplexed network data, processed through a micro Markov chain (MMC) model, to simulate the interplay between information spread and disease dynamics. The findings reveal a noteworthy positive correlation between the rates of information dissemination, recovery in the network, and the epidemic threshold. Conversely, the conversion rate is inversely related to this threshold. A critical observation is that Scale-free (SF) networks, characterized by their uneven node distribution, are more susceptible to the impacts of information spread on their outbreak thresholds compared to Erdős-Rényi (ER) networks. This research offers crucial insights for epidemic prevention strategies and provides valuable guidance for managing the dissemination of disease-related information within complex network structures.

Synchronization in the two time-scale multiplex network with symplectic interactions

Mounting experimental evidence suggests a significant role for glial cells, particularly astrocytes, in shaping neuronal activity in both cell cultures and the brain, driving interest in exploring multi-component network dynamics [1]. These systems are modeled at varying levels of physiological detail, ranging from the Hodgkin-Huxley and Ullah models for neurons and astrocytes, respectively, to simple integrate-and-fire models or phase oscillators. Multiplex networks are commonly used to model generic dynamical phenomena, with an emphasis on network connectivity effects rather than the complexity of an individual cell’s behavior. This model is particularly advantageous due to its use of a two-layer network structure [2]. This structure accurately describes neural connectivity through the long-range random coupling, while glial cells interact locally through the diffusion of mediatory molecules. Furthermore, the oscillatory timescales between neural and glial cells differ by at least one order of magnitude. In this context, the analysis of synchronization is a focal point as it is a crucial process that underpins information processing, decision making, and movement control in living neural systems [3]. Network topology is known to be essential, where all-to-all coupling and random Erdos–Renyi connectivity support the second-order phase transition to global phase coherence. In contrast, regular local coupling such as a 2D lattice only permits frequency and phase locking. Additionally, symplectic networks are capable of demonstrating a first-order phase transition, which is commonly referred to as “explosive” synchronization [4]. Recently, studies have shown that combining model neural (random) and glial (regular lattice) oscillatory layers can lead to a variety of outcomes [5]. Specifically, this combination was found to induce a second-order phase transition in the regular glial layer. In addition, synchronization in both layers may be preceded by desynchronization as the coupling between the layers becomes stronger. Here we investigate synchronization in the multiplex neural-glial network, where the neural layer is symplectic and contains triadic interactions. We demonstrate that symplectic coupling in the neural layer can induce the first order transition in the regular (glial) layer. Additionally, we show that such a transition can be induced by strengthening the glial and interlayer coupling, even if the symplectic neural layer alone is below the synchronization threshold. Desynchronization in the neuronal layer, resulting from the moderated coupling to the glial layer, never occurs abruptly.

Robustness analysis of edge-coupled interdependent networks under different attack strategies

The robustness of interdependent networks has been a focus of research on complex networks, and the issue of attacks has become a popular research topic. However, some existing works have revealed significant vulnerabilities in interdependent networks, and the research on its robustness has been limited to node-coupled networks. While in reality, many networks are edge-coupled, and their robustness analysis has been overlooked. This paper constructs edge-coupled networks with positive, negative and random coupling based on the characteristics of edge-coupled interdependent networks. The sublayers use Erdös–Rényi (ER) random networks and scale-free (SF) networks, and four attack strategies, which includes intentional node/edge attack and random node/edge attack, are used to analyze the robustness of different edge-coupled interdependent networks. Seven edge/node importance indicators are proposed by considering node betweenness centrality, degree and eigenvector centrality, and these indicators are applied to attack strategies for result analysis, corresponding methods for enhancing robustness are proposed. The analysis results indicate that under intentional attacks, networks with negative coupling exhibit the strongest robustness, and its robustness can be influenced by their sublayers. In an environment with 500 nodes and an average degree of 4, when there is an ER network in the sublayer, protecting nodes/edges with high degree can improve the robustness of networks. If the sublayers are only composed of many SF networks, the betweenness centrality will have a greater impact when attacking most edges. While under random attacks, the networks with positive coupling exhibit the strongest robustness.

The recoverability of network controllability with respect to node additions

Network controllability is a critical attribute of dynamic networked systems. Investigating methods to restore network controllability after network degradation is crucial for enhancing system resilience. In this study, we develop an analytical method based on degree distributions to estimate the minimum fraction of required driver nodes for network controllability under random node additions after the random removal of a subset of nodes. The outcomes of our method closely align with numerical simulation results for both synthetic and real-world networks. Additionally, we compare the efficacy of various node recovery strategies across directed Erdös–Rényi (ER) networks, swarm signaling networks (SSNs), and directed Barabàsi Albert (BA) networks. Our findings indicate that the most efficient recovery strategy for directed ER networks and SSNs is the greedy strategy, which considers node betweenness centrality. Similarly, for directed BA networks, the greedy strategy focusing on node degree centrality emerges as the most efficient. These strategies outperform recovery approaches based on degree centrality or betweenness centrality, as well as the strategy involving random node additions.

Root and community inference on the latent growth process of a network

Abstract Many statistical models for networks overlook the fact that most real-world networks are formed through a growth process. To address this, we introduce the Preferential Attachment Plus Erdős–Rényi model, where we let a random network G be the union of a preferential attachment (PA) tree T and additional Erdős–Rényi (ER) random edges. The PA tree captures the underlying growth process of a network where vertices/edges are added sequentially, while the ER component can be regarded as noise. Given only one snapshot of the final network G, we study the problem of constructing confidence sets for the root node of the unobserved growth process; the root node can be patient zero in an infection network or the source of fake news in a social network. We propose inference algorithms based on Gibbs sampling that scales to networks with millions of nodes and provide theoretical analysis showing that the size of the confidence set is small if the noise level of the ER edges is not too large. We also propose variations of the model in which multiple growth processes occur simultaneously, reflecting the growth of multiple communities; we use these models to provide a new approach to community detection.

Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks.

A Two-Phase Feature Selection Method for Identifying Influential Spreaders of Disease Epidemics in Complex Networks.

Network epidemiology plays a fundamental role in understanding the relationship between network structure and epidemic dynamics, among which identifying influential spreaders is especially important. Most previous studies aim to propose a centrality measure based on network topology to reflect the influence of spreaders, which manifest limited universality. Machine learning enhances the identification of influential spreaders by combining multiple centralities. However, several centrality measures utilized in machine learning methods, such as closeness centrality, exhibit high computational complexity when confronted with large network sizes. Here, we propose a two-phase feature selection method for identifying influential spreaders with a reduced feature dimension. Depending on the definition of influential spreaders, we obtain the optimal feature combination for different synthetic networks. Our results demonstrate that when the datasets are mildly or moderately imbalanced, for Barabasi-Albert (BA) scale-free networks, the centralities' combination with the two-hop neighborhood is fundamental, and for Erdős-Rényi (ER) random graphs, the centralities' combination with the degree centrality is essential. Meanwhile, for Watts-Strogatz (WS) small world networks, feature selection is unnecessary. We also conduct experiments on real-world networks, and the features selected display a high similarity with synthetic networks. Our method provides a new path for identifying superspreaders for the control of epidemics.