Identification Of Important Nodes Research Articles

Identification of important nodes in multi-layer hypergraphs based on fuzzy gravity model and node centrality distribution characteristics

Hyperedge is a common structure that represents high-order interactions between nodes in complex networks, and multi-layer networks provide more diverse node interactions than single-layer networks. Therefore, multi-layer hypergraphs can more clearly represent the relationships between nodes. However, there are few studies on identifying important nodes in this framework. This paper proposes a method called HCT to fill this gap. It consists of three parts, namely: Hypergraph Fuzzy Gravity Model (HFGM), Layer Weight Calculation Method based on Node Centrality Distribution Characteristics (CDLW) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). HCT progressively analyzes the importance of a node from three levels: local (the node itself), semi-local (the hyperedges and community to which the node belongs), and global (the layer to which the node belongs). By combining these three results, the global centrality of a node in the entire network can be calculated. Simulation experiments demonstrate that the important nodes identified by HCT exhibit stronger contagion capabilities in nine networks compared to nine combinatorial methods and removing these nodes will seriously damage the connectivity and robustness of the network. The centrality of each node calculated by HCT is also consistent with its actual importance.

Network analysis of gut microbial communities reveal key genera for a multiple sclerosis cohort with Mycobacterium avium subspecies paratuberculosis infection

BackgroundIn gut ecosystems, there is a complex interplay of biotic and abiotic interactions that decide the overall fitness of an individual. Divulging the microbe-microbe and microbe-host interactions may lead to better strategies in disease management, as microbes rarely act in isolation. Network inference for microbial communities is often a challenging task limited by both analytical assumptions as well as experimental approaches. Even after the network topologies are obtained, identification of important nodes within the context of underlying disease aetiology remains a convoluted task. We therefore present a network perspective on complex interactions in gut microbial profiles of individuals who have multiple sclerosis with and without Mycobacterium avium subspecies paratuberculosis (MAP) infection. Our exposé is guided by recent advancements in network-wide statistical measures that identify the keystone nodes. We have utilised several centrality measures, including a recently published metric, Integrated View of Influence (IVI), that is robust against biases.ResultsThe ecological networks were generated on microbial abundance data (n = 69 samples) utilising 16 S rRNA amplification. Using SPIEC-EASI, a sparse inverse covariance estimation approach, we have obtained networks separately for MAP positive (+), MAP negative (-) and healthy controls (as a baseline). Using IVI metric, we identified top 20 keystone nodes and regressed them against covariates of interest using a generalised linear latent variable model. Our analyses suggest Eisenbergiella to be of pivotal importance in MS irrespective of MAP infection. For MAP + cohort, Pyarmidobacter, and Peptoclostridium were predominately the most influential genera, also hinting at an infection model similar to those observed in Inflammatory Bowel Diseases (IBDs). In MAP- cohort, on the other hand, Coprostanoligenes group was the most influential genera that reduces cholesterol and supports the intestinal barrier.ConclusionsThe identification of keystone nodes, their co-occurrences, and associations with the exposome (meta data) advances our understanding of biological interactions through which MAP infection shapes the microbiome in MS individuals, suggesting the link to the inflammatory process of IBDs. The associations presented in this study may lead to development of improved diagnostics and effective vaccines for the management of the disease.

Dismantling complex networks with graph contrastive learning and multi-hop aggregation

Network dismantling is a process of identifying influential nodes that can decompose a network into disconnected sub-networks. This provides a novel approach to understanding and analyzing complex networks abstracted from the real world. State-of-the-art solutions for this task exploit graph encoders to capture the structural features of the network, which are then sent to the multi-layer perceptron for predicting the node importance. This process, however, fails to exploit the interactions among the graph representations learned from different views and neglects the neighboring information when evaluating node importance. In this work, we address these issues with a graph contrastive learning framework with multi-hop aggregation, resulting in the identification of influential nodes. Firstly, we construct role graphs to provide a holistic view of the original graphs. Secondly, graph representations are obtained in the individual views, and enhanced expressiveness is achieved through contrastive learning. Finally, based on the representations, the multi-hop neighbor information of the nodes is aggregated to rank the node importance, and thus aid in the identification of important nodes. We evaluate our proposal on real and synthetic networks, and the results show that our method outperforms the baseline with fewer nodes required to disassemble a network.

MGL2Rank: Learning to rank the importance of nodes in road networks based on multi-graph fusion

The identification of important nodes with strong propagation capabilities in road networks is a vital topic in urban planning. Existing methods for evaluating the importance of nodes in traffic networks only consider topological information and traffic volumes, the diversity of the traffic characteristics in road networks, such as the number of lanes and average speed of road segments, is ignored, thus limiting their performance. To solve this problem, we propose a graph learning-based framework (MGL2Rank) that integrates the rich characteristics of road networks to rank the importance of nodes. This framework comprises an embedding module containing a sampling algorithm (MGWalk) and an encoder network to learn the latent representations for each road segment. MGWalk utilizes multi-graph fusion to capture the topology of road networks and establish associations between road segments based on their attributes. The obtained node representation is then used to learn the importance ranking of the road segments. Finally, a synthetic dataset is constructed for ranking tasks based on the regional road network of Shenyang City, and the ranking results on this dataset demonstrate the effectiveness of our method. The data and source code for MGL2Rank are available at https://github.com/ZJ726.

Identifying critical nodes in complex networks based on neighborhood information

The identification of important nodes in complex networks has always been a prominent topic in the field of network science. Nowadays, the emergence of large-scale networks has sparked our research interest in complex network centrality methods that balance accuracy and efficiency. Therefore, this paper proposes a novel centrality method called Spon (Sum of the Proportion of Neighbors) Centrality, which combines algorithmic efficiency and accuracy. Spon only requires information within the three-hop neighborhood of a node to assess its centrality, thereby exhibiting lower time complexity and suitability for large-scale networks. To evaluate the performance of Spon, we conducted connectivity tests on 16 empirical unweighted networks and compared the monotonicity and algorithmic efficiency of Spon with other methods. Experimental results demonstrate that Spon achieves both accuracy and algorithmic efficiency, outperforming eight other methods, including CycleRatio, collective influence, and Social Capital. Additionally, we present a method called W-Spon to extend Spon to weighted networks. Comparative experimental results on 10 empirical weighted networks illustrate that W-Spon also possesses advantages compared to methods such as I-Core and M-Core.

Identifying important nodes in complex networks based on extended degree and E-shell hierarchy decomposition

The identification of important nodes is a hot topic in complex networks. Many methods have been proposed in different fields for solving this problem. Most previous work emphasized the role of a single feature and, as a result, rarely made full use of multiple items. This paper proposes a new method that utilizes multiple characteristics of nodes for the evaluation of their importance. First, an extended degree is defined to improve the classical degree. And E-shell hierarchy decomposition is put forward for determining nodes’ position through the network’s hierarchical structure. Then, based on the combination of these two components, a hybrid characteristic centrality and its extended version are proposed for evaluating the importance of nodes. Extensive experiments are conducted in six real networks, and the susceptible–infected–recovered model and monotonicity criterion are introduced to test the performance of the new approach. The comparison results demonstrate that the proposed new approach exposes more competitive advantages in both accuracy and resolution compared to the other five approaches.

Identification of Important Nodes in Multilayer Heterogeneous Networks Incorporating Multirelational Information

Centrality is an effective method to identify important nodes in complex networks, but it is still a challenge to find influential nodes by making full use of multiple relationships and global network topological features in complex networks. To address these problems, this article proposes an importance identification method for multilayer heterogeneous network node by incorporating multirelational information (MLC). This method studies the relational characteristics of heterogeneous nodes in detail and divides the heterogeneous nodes into different layers according to the node types, which can be further divided into core and auxiliary layers. The importance of the auxiliary layer is quantified by designing the interlayer influence and determining the interlayer influence weights of different connectivity influences; the centrality score of heterogeneous nodes under multiconnectivity relationships is fused using the transmission characteristics of internode relationships in the auxiliary layer, which in turn measures the importance of nodes in the core layer. To evaluate the proposed algorithm, we conduct experiments on five real multilayer heterogeneous networks of different sizes. The results show that MLC can make full use of different types of internode association relationship information, effectively fuse network structure information such as the neighbor weights of core and auxiliary layer nodes, and outperform the existing techniques in identifying important nodes.

Importance evaluation of power network nodes based on community division and characteristics of coupled network

The identification of important nodes in the power and communication coupling network is beneficial to prevent the occurrence of cascading failures. It is of great significance to establish a robust and resilient coupling network. This paper proposes a new method for evaluating the importance of power information network nodes based on link-based community division and Betweenness Centrality Based on Neighbor Nodes (BCBNN) algorithm to prevent better power grid cascading failures. This method can evaluate the importance of nodes in the network, except the nodes whose node betweenness is zero. First of all, this article uses the link-based dividing method explores the overlapping communities in the power grid; secondly, it calculates the importance of nodes in a single-layer network based on BCBNN algorithm; finally, it proposes a characteristic node importance assessment method considering single-layer network topology, grid overlapping structure and dual-network coupling. In addition, this paper has conducted experiments on the standard IEEE30-node system and improved IEEE30-node system. Compared with the node shrinkage method and Max-Cas algorithm, the experimental results not only identify traditional nodes, but also mines potential nodes that could cause the grid to fail. It means that the proposed algorithm has a better degree of differentiation in terms of importance assessment.

Identifying important nodes for temporal networks based on the ASAM model

The identification of important nodes in a temporal network is of great significance for the analysis and control of the information dissemination process. In this work, the multi-layer coupled network analysis method is employed to identify important nodes in a temporal network. First, to overcome the problem of a fixed constant being unable to reflect differences in the inter-layer coupling relationship, and by combining a node’s own neighbors and common neighbors of nodes in two-time layers, a new Enhanced Similarity Index (ESI) is proposed to measure the inter-layer coupling relationship. Secondly, the attenuation factor is introduced to more accurately describe the inter-layer coupling relationship. Finally, an Attenuation-Based Supra-Adjacency Matrix (ASAM) temporal network modeling method based on the attenuation of the inter-layer coupling strength is proposed. The importance of nodes in the temporal network is evaluated by calculating the eigenvector centrality of the nodes in each time layer in the temporal network. It is found that after deleting a certain percentage of the important nodes identified by the ASAM method, the temporal Largest Connected Component (LCC) of the network becomes smaller, and the network performance is improved as compared with the SAM and SSAM methods. The results indicate that the important nodes identified by the ASAM are at the core of the network and have a greater impact on the network structure and functions. This demonstrates that the proposed ASAM model can more effectively identify important nodes in the temporal network, and has significant application value in this research field.

Temporal gravity model for important node identification in temporal networks

• We define important nodes as those with high structural influence and/or spreading influence. • Motivated by classic gravity, we propose a temporal gravity model to identify important nodes in temporal networks. • Model captures the temporal evolution of networks in the identification of important nodes. • The high performance of the proposed model over the direct use of centrality metrics. Identifying important nodes in networks is essential to analysing their structure and understanding their dynamical processes. In addition, myriad real systems are time-varying and can be represented as temporal networks. Motivated by classic gravity in physics, we propose a temporal gravity model to identify important nodes in temporal networks. In gravity, the attraction between two objects depends on their masses and distance. For the temporal network, we treat basic node properties (e.g., static and temporal properties) as the mass and temporal characteristics (i.e., fastest arrival distance and temporal shortest distance) as the distance. Experimental results on 10 real datasets show that the temporal gravity model outperforms baseline methods in quantifying the structural influence of nodes. When using the temporal shortest distance as the distance between two nodes, the proposed model is more robust and more accurately determines the node spreading influence than baseline methods. Furthermore, when using the temporal information to quantify the mass of each node, we found that a novel robust metric can be used to accurately determine the node influence regarding both network structure and information spreading.

Identifying influential nodes in complex networks: Effective distance gravity model

The identification of important nodes in complex networks is an area of exciting growth due to its applications across various disciplines like disease control, data mining and network system control. Many measures have been proposed to date, but they are either based on the locality of nodes or the global nature of the network. These measures typically use the traditional Euclidean Distance, which only focuses on local static geographic distance between nodes but ignores the dynamic interaction between nodes in real-world networks. Both the static and dynamic information should be considered for the purpose of identifying influential nodes. In order to address this problem, we have proposed an original and novel gravity model with effective distance for identifying influential nodes based on information fusion and multi-level processing. Our method is able to comprehensively consider the global and local information of complex networks, and also utilizes the effective distance to incorporate static and dynamic information. Moreover, the proposed method can help us mine for hidden topological structure of real-world networks for more accurate results. The susceptible infected model, Kendall correlation coefficient and eight existing identification methods are utilized to carry out simulations on twelve different real networks.

Centrality measures for node-weighted networks via line graphs and the matrix exponential

This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.

An empirical evaluation of the influential nodes for stock market network: Chinese A-shares case

This paper aims to rank the influential nodes for Chinese A-share market by employing complex network analysis approach. More than one hundred directed weighted stock market networks are constructed by the methods of Engle-Granger test, Granger Causality test and moving window among 847 stocks for the time period from January 2006 to June 2019. Then the identification of important nodes is investigated by using weighted LeaderRank algorithm. The results show that: (i) the average clustering coefficient and global efficiency increase sharply in the run-up to, and during the financial crisis, and decline rapidly afterwards. (ii) 66.98% of stock market networks have scale-free property. (iii) the influential companies are generally large-capitalization companies. In addition, an interesting finding is that, top 3 influential stocks are high price stocks which are so called “hundred shares” by Chinese investors.

An artificial intelligence based method for evaluating power grid node importance using network embedding and support vector regression

The identification of important nodes in a power grid has considerable benefits for safety. Power networks vary in many aspects, such as scale and structure. An index system can hardly cover all the information in various situations. Therefore, the efficiency of traditional methods using an index system is case-dependent and not universal. To solve this problem, an artificial intelligence based method is proposed for evaluating power grid node importance. First, using a network embedding approach, a feature extraction method is designed for power grid nodes, considering their structural and electrical information. Then, for a specific power network, steady-state and node fault transient simulations under various operation modes are performed to establish the sample set. The sample set can reflect the relationship between the node features and the corresponding importance. Finally, a support vector regression model is trained based on the optimized sample set for the later online use of importance evaluation. A case study demonstrates that the proposed method can effectively evaluate node importance for a power grid based on the information learned from the samples. Compared with traditional methods using an index system, the proposed method can avoid some possible bias. In addition, a particular sample set for each specific power network can be established under this artificial intelligence based framework, meeting the demand of universality.

Robustness Evaluation Strategy of Ubiquitous Power Internet of Things Based on Important Node Recognition

This paper analyses the structure and characteristics of ubiquitous power Internet of things (UP-IoT) from four levels: the perception layer, network layer, platform layer and application layer. The robustness of UP-IoT is defined from the perspective of system structure, and the internal and external disturbance factors of robustness are analysed. According to the scale-free characteristics of complex network, a robustness evaluation strategy for UP-IoT based on identification of important nodes is proposed. A set of robustness evaluation indexes, including degree centrality, betweenness centrality, closeness centrality, maximum connectivity and connectivity factors, are established to quantify the importance of nodes. The model in this paper is used to analyse the UP-IoT network model with 12 nodes and verify the feasibility of the evaluation strategy.

Voltage stability assessment and identification of important nodes in power transmission network through network response structural characteristics

Electrical power grids are often susceptible to voltage instability and have been a growing concern. In this study, the authors propose techniques based on network response structural characteristics for voltage stability assessment and for the identification of important nodes in electrical power grids. First, the network response structural characteristic indices (NRSCIs) which are inherent in the conventional power grids in terms of the Kirchhoff matrix is formulated. The eigenvalue decomposition (ED) technique is then applied to a submatrix of the Kirchhoff matrix to determine the topological strength of the electrical network graph. The vertex (node) that has a minimum eigenvalue is taken as the critical mode, from which its contributions to the entire graph is identified using the proposed network response structural characteristics theory participation factor (NRSCTPF). To demonstrate the magnitude of the concept formulated, the known degree centrality is modified in terms of the established NRSCI, which are then used to determine the important nodes of the network graph. The results obtained show that the proposed NRSCTPF and the degree centrality based on the NRSCI can be used for voltage stability assessment and identification of important nodes. The proposed approach is also less computationally intensive compared with the traditional approach.

A Novel Multi-Indicator Evaluation Algorithm for Identifying the Important Nodes in Complex Networks

Identification of important nodes is an emerging hot topic in complex networks over the last few years. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness, closeness, etc. At present, most algorithms of important node evaluation are based on the single-indicator, which can't reflect the whole condition of the complex network. Therefore, in this paper, after choosing multiple indicators from degree centrality, closeness centrality, eigenvector centrality, information centrality, density/clustering coefficient, mutual-information centrality, etc., and a new multi-indicator evaluation algorithm based on Locally Linear Embedding (LLE) for identifying important nodes in complex network is proposed. This proposed algorithm is compared with some single-indicator algorithms and other mainstream multi-indicator algorithms based on real-world networks. Through comprehensive analysis, the experimental results show that the proposed method performs quite well in evaluating the importance of nodes, and it is rational, effective, integral and accurate.

Identification of important nodes in directed biological networks: a network motif approach.

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.

Identification and Evolution of Structurally Dominant Nodes in Protein-Protein Interaction Networks

It is well known that protein-protein interaction (PPI) networks are typical evolving complex networks. Identification of important nodes has been an emerging popular topic in complex networks. Many indexes have been proposed to measure the importance of nodes in complex networks, such as degree, closeness, betweenness, k-shell, clustering coefficient, semi-local centrality, eigenvector centrality. Based on multivariate statistical analysis, through integrating the above indexes and further considering the appearances of nodes in network motifs, this paper aims at developing a new measure to characterize the structurally dominant proteins (SDP) in PPI networks. Moreover, we will further investigate the evolution of the defined dominant nodes in temporal evolving real-world and artificial PPI networks. Our results indicate that the constructed artificial networks have some similar statistical properties as those of the real-world evolving networks. In this case, the artificial PPI networks can be used to further investigate the above evolution characteristics of the real-world evolving networks. Simulation results reveal that SDP in the yeast PPI networks are evolutionary conserved, however, the undominant nodes evolve rapidly. Furthermore, PPI networks are very robust against random mutations, while fragile yet with certain robustness to targeted mutations on SDP. Our investigations shed some light on the future applications of the evolving characteristics of bio-molecular networks, such as reengineering of particular networks for technological, synthetic or pharmacological purposes.

Identifying important nodes in weighted functional brain networks: A comparison of different centrality approaches

We compare different centrality metrics which aim at an identification of important nodes in complex networks. We investigate weighted functional brain networks derived from multichannel electroencephalograms recorded from 23 healthy subject under resting-state eyes-open or eyes-closed conditions. Although we observe the metrics strength, closeness, and betweenness centrality to be related to each other, they capture different spatial and temporal aspects of important nodes in these networks associated with behavioral changes. Identifying and characterizing of these nodes thus benefits from the application of several centrality metrics.