Real Complex Networks Research Articles

Identifying influential spreaders in complex networks based on limited spreading domain

In recent years, the problem of influential spreader identification in complex networks has attracted extensive attention as its fundamental role in social network analysis, rumor controlling, viral marketing and other related fields. Centrality measures that consider different scales of neighborhood are commonly utilized for ranking node influence. The 2-hop neighborhood of the target node is deemed a suitable evaluation metric. However, as the network scale expands, only considering 2-hop neighborhood is overly restrictive. Furthermore, the interconnections among nodes are often disregarded. In this article, a new method named Limited Spreading Domain (LSD) is proposed to identify influential spreaders. LSD defines the target node’s 2-hop neighborhood as basic domain and takes the neighbors who are 3–6 hops away from target node as extended domain. The influence of target node is modeled as diffusion along the paths with limited length in basic domain and extended domain. A series of experiments are conducted in eight real complex networks and results demonstrate that LSD outperforms common centralities in terms of accuracy, stability,distinguishability and scalability.

Fast Markov Clustering Algorithm Based on Belief Dynamics.

Graph clustering is one of the most significant, challenging, and valuable topic in the analysis of real complex networks. To detect the cluster configuration accurately and efficiently, we propose a new Markov clustering algorithm based on the limit state of the belief dynamics model. First, we present a new belief dynamics model, which focuses beliefs of multicontent and randomly broadcasting information. A strict proof is provided for the convergence of nodes' normalized beliefs in complex networks. Second, we introduce a new Markov clustering algorithm (denoted as BMCL) by employing a belief dynamics model, which guarantees the ideal cluster configuration. Following the trajectory of the belief convergence, each node is mapped into the corresponding cluster repeatedly. The proposed BMCL algorithm is highly efficient: the convergence speed of the proposed algorithm researches O(TN) in sparse networks. Last, we implement several experiments to evaluate the performance of the proposed methods.

LSS: A locality-based structure system to evaluate the spreader’s importance in social complex networks

Assessing the importance of spreaders in networks is crucial for investigating the survival and robustness of networks. There are numerous potential applications, such as preventing outbreaks, spreading viruses on computer networks, viral marketing, and sickness spreading. These problems are usually unable to be solved by many heuristics with low time complexity. A number of tentative heuristics have been proposed for different application scenarios. However, we still lack an efficient heuristic to solve this type of problem effectively, for instance, low rating accuracy or high time complexity. To deal with this issue, this paper proposes a new heuristic called Locality-based Structure System (LSS), which is based on local information rather than global information of nodes in a network to determine the importance of spreaders. The proposed LSS takes into account the k-shell, degree, and number of triangles in a network. First, connectivity factors are computed based on the properties of nodes connected to them. Then, each node’s contribution to the importance of lines is computed. Finally, the degree and k-shell of nodes, as well as their contribution to the importance of lines, are taken into account. The proposed LSS is validated on a set of real and synthetic complex networks, where the simulation results under the standard SIR model and Kendall correlation coefficient indicate that LSS can efficiently identify influential spreaders in numerous types of networks without requiring any advanced parameter settings.

Influential nodes identification method based on adaptive adjustment of voting ability

Influential nodes identification technology is one of the important topics which has been widely applied to logistics node location, social information dissemination, transportation network carrying, biological virus dissemination, power network anti-destruction, etc. At present, a large number of influential nodes identification methods have been studied, but the algorithms that are simple to execute, have high accuracy and can be better applied to real networks are still the focus of research. Therefore, due to the advantages of simple to execute in voting mechanism, a novel algorithm based on adaptive adjustment of voting ability (AAVA) to identify the influential nodes is presented by considering the local attributes of node and the voting contribution of its neighbor nodes, to solve the problem of low accuracy and discrimination of the existing algorithms. This proposed algorithm uses the similarity between the voting node and the voted node to dynamically adjust its voting ability without setting any parameters, so that a node can contribute different voting abilities to different neighbor nodes. To verify the performance of AAVA algorithm, the running results of 13 algorithms are analyzed and compared on 10 different networks with the SIR model as a reference. The experimental results show that the influential nodes identified by AAVA have high consistency with SIR model in Top-10 nodes and Kendall correlation, and have better infection effect of the network. Therefore, it is proved that AAV algorithm has high accuracy and effectiveness, and can be applied to real complex networks of different types and sizes.

Maximally modular structure of growing hyperbolic networks

Hyperbolic network models provide a particularly successful approach to explain many peculiar features of real complex networks including, for instance, the small-world and scale-free properties, or the relatively high clustering coefficient. Here we show that for the popularity-similarity optimisation (PSO) model from this family, the generated networks become also extremely modular in the thermodynamic limit, despite lacking any explicitly built-in community formation mechanism in the model definition. In particular, our analytical calculations indicate that the modularity in PSO networks can get arbitrarily close to its maximal value of 1 as the network size is increased. We also derive the convergence rate, which turns out to be dependent on the popularity fading parameter controlling the degree decay exponent of the generated networks.

A novel network core structure extraction algorithm utilized variational autoencoder for community detection

Community detection technologies have the general research significance in complex networks, in which the topology information of network is worthy to be the focus for its widely application. It is the definition of community structure that the connection of nodes in the community is dense with the connection of nodes outside the community is sparse, which is corresponding to the core structure in the complex real networks is represented by a compact and dense set of connected nodes. While all the notes in the network are considered by the traditional topology, it is hard to extract the core structure with the continuous, exponential growth of community networks. In this paper, a novel network core structure extraction algorithm utilized variational autoencoder for community detection(CSEA) is proposed for finding the community structure more accurately. Firstly, the K-truss algorithm is used to find the core structure information in the network, and the similarity matrix is generated by similarity mapping combined with local information. Secondly, the variational autoencoder is used to extract and reduce the dimension of the similarity matrix containing the core structure of the network, and the low-dimensional feature matrix is obtained. Finally, the K-means clustering algorithm is utilized to obtain the community structure information. We compare CSEA algorithm with 18 different types of community detection algorithms using 4 evaluation metrics on 19 complex real networks. By extensively evaluating our algorithm on large real-world datasets, we show that CSEA algorithm has an excellent community division effect in dense complex real networks, especially in small and medium-sized networks, and it can accurately divide the complex real networks with unknown community structure. Simultaneously, CSEA algorithm also reveals some efficiency advantage in its on-line test.

An efficient weighted network centrality approach for exploring mechanisms of action of the Ruellia herbal formula for treating rheumatoid arthritis

AimThis study outlines an efficient weighted network centrality measure approach and its application in network pharmacology for exploring mechanisms of action of the Ruellia prostrata (RP) and Ruellia bignoniiflora (RB) herbal formula for treating rheumatoid arthritis.MethodIn our proposed method we first calculated interconnectivity scores all the network targets then computed weighted centrality score for all targets to identify of major network targets based on centrality score. We apply our technology to network pharmacology by constructing herb-compound-putative target network; compound-putative targets-RA target network; and imbalance multi-level herb-compound-putative target-RA target-PPI network. We then identify the major targets in the network based on our centrality measure approach. Finally we validated the major identified network targets using the enrichment analysis and a molecular docking simulation.ResultThe results reveled our proposed weighted network centrality approach outperform classical centrality measure in identification of influential nodes in four real complex networks based on SI model simulation. Application of our approach to network pharmacology shows that 57 major targets of which 33 targets including 8 compositive compounds, 15 putative target and 10 therapeutic targets played an important role in the network and directly linked to rheumatoid arthritis. Enrichment analysis confirmed that putative targets were frequently involved in TNF, CCR5, IL-17 and G-protein coupled receptors signaling pathways which are critical in the progression of rheumatoid arthritis. The molecular docking simulation indicated four targets had significant binding affinity to major protein targets. Glyceryl diacetate-2-Oleate and Oleoyl chloride showed the best binding affinity to all targets proteins and were within Lipinski limits. ADMET prediction also confirm both compounds had no toxic effect on human hence potential lead drug compounds for treating rheumatoid arthritis.ConclusionThis study developed an efficient weighted network centrality approach as tool for identification of major network targets. Network pharmacology findings provides promising results that could lead us to design and discover of alternative drug compounds. Though our approach is a purely in silico method, clinical experiments are required to test and validate the hypotheses of our computational methods.

Multiscale voter model on real networks

We introduce the Multiscale Voter Model (MVM) to investigate clan influence at multiple scales—family, neighborhood, political party…—in opinion formation on real complex networks. Clans, consisting of similar nodes, are constructed using a coarse-graining procedure on network embeddings that allows us to control for the length scale of interactions. We ran numerical simulations to monitor the evolution of MVM dynamics in real and synthetic networks, and identified a transition between a final stage of full consensus and one with mixed binary opinions. The transition depends on the scale of the clans and on the strength of their influence. We found that enhancing group diversity promotes consensus while strong kinship yields to metastable clusters of same opinion. The segregated domains, which signal opinion polarization, are discernible as spatial patterns in the hyperbolic embeddings of the networks. Our multiscale framework can be easily applied to other dynamical processes affected by scale and group influence.

A Simplified Quantum Walk Model for Predicting Missing Links of Complex Networks.

Prediction of missing links is an important part of many applications, such as friends' recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein-protein networks.

Density-Peak-Based Overlapping Community Detection Algorithm

Overlapping community detection is essential for revealing the hidden structure of complex networks. In this work, we present an overlapping community detection algorithm that selects community centers adaptively based on density peaks. The proposed algorithm, called the density-peak-based overlapping community detection (DPOCD) algorithm, defines point link strength and edge link strength to construct distance matrix. Unlike the density peaks clustering algorithm, by which cluster centers are selected manually, the DPOCD algorithm uses the linear fitting method to select community centers. To evaluate the feasibility of the presented algorithm, we compared it with other advanced methods on artificial synthetic network and real complex network datasets. The experimental results demonstrate that our method achieves excellent performance in large-scale complex networks and the robustness of the algorithm.

Hyperbolic disc embedding of functional human brain connectomes using resting-state fMRI.

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging, we constructed a scale-free binary graph for each subject, using internodal time series correlation of regions of interest as a proximity measure. The resulting network could be embedded onto manifolds of various curvatures and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using the 𝕊1/ℍ2 model, we reduced the dimension of the network into two-dimensional hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed relevance with its anatomic counterpart and absence of center-spaced node. Using the hyperbolic distance on the 𝕊1/ℍ2 model, we could detect the anomaly of network in autism spectrum disorder subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.

Stability in star networks of identical Stuart–Landau oscillators with asymmetric coupling

In this paper, we systematically investigate the stability issues of different kinds of collective behaviors, including the equilibrium point, complete synchronization, quenched hub incoherence, anti-phase remote synchronization and regular remote synchronization, which arise in identical Stuart–Landau oscillators asymmetrically coupled in a star network. We have analytically obtained their rigorous stability conditions and stable basins, which are well verified by numerical results. Additionally, we surprisingly find that, for measuring the remote synchronization, the two traditional order parameters rdirect and rindirect are not well-defined metrics. All these results may help us to further improve our understanding of nonlinear systems’ complete, partial and cluster synchronization behaviors in real or man-made complex networks.

Machine Learning‐Based Surrogate Modeling for Urban Water Networks: Review and Future Research Directions

AbstractSurrogate models replace computationally expensive simulations of physically‐based models to obtain accurate results at a fraction of the time. These surrogate models, also known as metamodels, have been employed for analysis, control, and optimization of water distribution and urban drainage systems. With the advent of machine learning (ML), water engineers have increasingly resorted to these data‐driven techniques to develop metamodels of urban water networks (UWNs). In this article, we review 31 recent articles on ML‐based metamodeling of UWNs to outline the state‐of‐the‐art of the field, identify outstanding gaps, and propose future research directions. For each article, we critically examined the purpose of the metamodel, the metamodel characteristics, and the applied case study. The review shows that current metamodels suffer several drawbacks, including (a) the curse of dimensionality, hindering implementation for large case studies; (b) black‐box deterministic nature, limiting explainability and applicability; and (c) rigid architecture, preventing generalization across multiple case studies. We argue that researchers should tackle these issues by resorting to recent advancements in ML concerning inductive biases, robustness, and transferability. Recently developed neural network architectures, which extend deep learning methods to graph data structures, are preferred candidates for advancing surrogate modeling in UWNs. Furthermore, we foresee increasing efforts for complex applications where metamodels may play a fundamental role, such as uncertainty analysis and multi‐objective optimization. Lastly, the development and comparison of ML‐based metamodels can benefit from the availability of new benchmark datasets for urban drainage systems and realistic complex networks.

Locally Expansion Directed Community Detection Method Considering Node Leadership

In recent years, community structure has become a research hotspot in complex networks, and there are currently many excellent methods in the field of community detection, such as label propagation algorithms, LFM community detection algorithms, etc. These algorithms primarily investigate undirected networks, but the linking relationships between nodes in real complex networks are mostly directed and asymmetric, such as social networks. Therefore it is imperative to perform community detection on directed networks. We proposed a locally expansion community detection algorithm (DLE-NL) that can be applied to directed networks. There are four essential parts of DLE-NL algorithm: Firstly, the node cross-leadership index is proposed to select seed nodes considering local and global factors and directionality; secondly, seed node confidants are chosen to form the initial community using node following degree, and the core of the community is precisely mined; then node aggregation is carried out considering the node affiliation to the community with the initial community as the core. Finally, the initial reconstruction and optimization of the community are carried out by removing communities with less than three nodes, correcting the affiliation of nodes to the community based on the community directed-fitness function and the gain of the derivative, assigning free nodes and merging communities with high similarity. The experimental results show that the method performs well in the directed modularity and normalized mutual information metrics, while the community detection results are more stable.

TOPOLOGICAL AND DYNAMICAL PROPERTIES OF THE NETWORK OF SHAREHOLDERS IN S&P 500 COMPANIES BASED ON GRAPH DATABASES

The interesting properties of scale-free and small-world networks recently observed have triggered the attention of the research community to the study of real growing complex networks. In scale-free networks, most vertices are sparsely connected, while a few vertices are intensively connected to many others, indicating a “preferential linking” during growing. In small-world networks, the average length of the shortest path between two randomly chosen nodes is small. In this paper, we study the topological and dynamical properties of the network of shareholders (NOS) in 11593 different companies. Based on Graph Databases, we calculate all the well-known in the literature topological and dynamical properties of a network along with centrality measures of nodes of NOS, which quantify the role that a node plays in the overall structure of NOS. We prove that NOS is both a scale-free and smallworld network. An understanding of NOS helps in predicting the emergence of important new phenomena affecting portfolio management in general. Also, this work reveals the fact that graph databases could serve as an efficient tool for analyzing such network models for stock markets. To the best of the authors’ knowledge, this is the first study calculating all the well-known in the literature topological and dynamical properties for Market Investments Networks, that is based on graph databases.

Reliability analysis of complex water distribution systems: the role of the network connectivity and tanks

Abstract A reliable water distribution network (WDN) can provide an adequate supply service to customers under both normal and abnormal working conditions. The WDN reliability analysis, therefore, is a keystone to improve the supply service efficiency. Strategies for reliability analysis are usually proved on small WDNs, which do not compare with large real complex systems in terms of number of water tanks, pressure reduction valves, variable speed pumps, controlled devices and possible alternative water supply schemes. The topological changes due to pipeline interruptions impact on emptying–filling of water tanks and network pressure status. This work proposes a two-level procedure for mechanical reliability assessment, suited for large real WDNs. It leverages a path/connectivity-based approach to set up reliability indicators for global-level analysis and local screening of the most critical scenarios. The employed advanced hydraulic model includes the automatic detection of topological changes and the robust modelling of water level in tanks using the generalized global gradient algorithm. The extended period simulation enables the reliability assessment of alternative water supply schemes and the sensitivity of tanks and controlled devices to single failure events. The procedure is demonstrated on a real complex network, being consistent with the ongoing digital transition in the WDN management sector.

An Efficient Partition-Based Approach to Identify and Scatter Multiple Relevant Spreaders in Complex Networks.

One of the main problems in graph analysis is the correct identification of relevant nodes for spreading processes. Spreaders are crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases, rumors, and more. Correct identification of spreaders in graph analysis is a relevant task to optimally use the network structure and ensure a more efficient flow of information. Additionally, network topology has proven to play a relevant role in the spreading processes. In this sense, more of the existing methods based on local, global, or hybrid centrality measures only select relevant nodes based on their ranking values, but they do not intentionally focus on their distribution on the graph. In this paper, we propose a simple yet effective method that takes advantage of the underlying graph topology to guarantee that the selected nodes are not only relevant but also well-scattered. Our proposal also suggests how to define the number of spreaders to select. The approach is composed of two phases: first, graph partitioning; and second, identification and distribution of relevant nodes. We have tested our approach by applying the SIR spreading model over nine real complex networks. The experimental results showed more influential and scattered values for the set of relevant nodes identified by our approach than several reference algorithms, including degree, closeness, Betweenness, VoteRank, HybridRank, and IKS. The results further showed an improvement in the propagation influence value when combining our distribution strategy with classical metrics, such as degree, outperforming computationally more complex strategies. Moreover, our proposal shows a good computational complexity and can be applied to large-scale networks.

Internet-like brain hierarchical network model: Alzheimer's disease study as an example

Background and ObjectiveThe modular structure and hierarchy are important topological characteristics in real complex networks such as brain networks on temporal scale. However, there are few studies investigating the hierarchical structure at the spatial scale of brain networks, the application of which still remains to be further studied. MethodsIn this study, a novel model of brain hierarchical network based on the hierarchical characteristic of Internet topology is proposed for the first time, which is called Internet-like brain hierarchical network (IBHN). In this model, the whole brain network is partitioned into multiple levels: brain wide area network (Brain-WAN), brain metropolitan network (Brain-MAN), and brain local area network (Brain-LAN). A Brain-MAN is formed by the interconnection of multiple Brain-LANs, and the interconnection of multiple Brain-MANs forms a Brain-WAN. A multivariate analysis method is employed to measure overall functional connectivity between two brain networks at the same network level rather than detecting the change of each node pair's functional connection. Furthermore, we demonstrate the utility of IBHN model with application to a practical case-control study involving 64 patients with Alzheimer's disease and 75 healthy controls. ResultsThe proposed model identified enhanced functional connectivity (P-value<0.05) at Brain-WAN level and reduced functional connectivity (P-value=0.004) at Brain-LAN level of Alzheimer's disease patients, which can be used as a multi-dimension functional reference for AD's diagnosis. ConclusionsThis study not only provides insight into AD pathophysiology, but also further proves the effectiveness of the proposed IBHN model. In addition, the IBHN model makes it possible to explore the brain's functional organization from multiple dimensions and offers a multi-level perspective for the research of complex brain network.

Scale-free Characteristics and Link Prediction in Complex Railway Network

The link-prediction of complex networks is a new method of network structure mining, which is different from the traditional methods based on machine learning. It reveals those existing relations and predicts possible ones, by using the similarity index of network structure. This paper studied the topology of the railway and link-prediction. The railway dataset was firstly obtained by sampling and pre-processing. Its degree obeys the power-law distribution with the scale-free characteristics. Then, we give some predictions for railway networks. These tests reached good prediction accuracy. The research result has demonstrated that the topological structure of network could be better choice to the link-prediction of a real complex networks.

Cliques Are Bricks for k-CT Graphs

Many real networks in biology, chemistry, industry, ecological systems, or social networks have an inherent structure of simplicial complexes reflecting many-body interactions. Over the past few decades, a variety of complex systems have been successfully described as networks whose links connect interacting pairs of nodes. Simplicial complexes capture the many-body interactions between two or more nodes and generalized network structures to allow us to go beyond the framework of pairwise interactions. Therefore, to analyze the topological and dynamic properties of simplicial complex networks, the closed trail metric is proposed here. In this article, we focus on the evolution of simplicial complex networks from clicks and k-CT graphs. This approach is used to describe the evolution of real simplicial complex networks. We conclude with a summary of composition k-CT graphs (glued graphs); their closed trail distances are in a specified range.