Node Ranking Research Articles

Development of a multidimensional centrality metric for ranking nodes in complex networks

Ranking nodes in complex networks is a fundamental task in network science, with significant applications in fields like social networks, bioinformatics, and information dissemination. Many existing methods struggle to efficiently capture the multifaceted relationships between nodes, particularly in large-scale networks. However, they often ignore the semantic relationships between nodes when gathering information. To address these challenges, this paper introduces SAASP, a Semi-local centrality measure that combines an Augmented graph with Average Shortest Path theory to efficiently identify influential nodes in complex networks. In SAASP, the augmented graph can represent global relationships between nodes as semantic similarities, allowing distant relationships to be considered in node ranking. Additionally, it incorporates an enhanced version of average shortest path theory to handle the computational complexity associated with large networks. By extracting local subgraphs for each node and considering the extended neighborhood concept, SAASP ensures scalability while preserving key structural properties. The integration of the augmented graph and average shortest path theory enables SAASP to accurately and efficiently identify influential nodes in large-scale complex networks with lower complexity. The effectiveness of the proposed metric is demonstrated through extensive experiments using the SIR (Susceptible-Infected-Removed) model and Kendall's coefficient, where it outperforms existing centrality measures on real-world datasets.

Graph neural link predictor based on cycle structure

AbstractCurrently, the link prediction algorithms primarily focus on studying the interaction between nodes based on chain structure and star structure, which predominantly rely on low‐order structural information and do not explore the multivariate interactions between nodes from the perspective of higher‐order structural information present in the network. The cycle structure is a higher‐order structure that lies between the star and clique structures, where all nodes within the same cycle can interact with each other, even in the absence of direct edges. If a node is encompassed by multiple cycles, it indicates that the node interacts and associates with a greater number of nodes in the network, and it means the node is more important in the network to some extent. Furthermore, if two nodes are included in multiple cycles, it signifies the two nodes are more likely to be connected. Therefore, firstly, a multi‐information fusion node importance algorithm based on the cycle structure information is proposed, which integrates both high‐order and low‐order structural information. Secondly, the obtained integrated structure information and node feature information is regarded as the input features, a two‐channel graph neural network model is designed to learn the cycle structure information. Then, the cycle structure information is utilised for the task of link prediction, and a graph neural link predictor with multi‐information interactions based on the cycle structure is developed. Finally, extensive experimental validation and analysis show that the node ranking result of the proposed node importance index is more consistent with the actual situation, the proposed graph neural network model can effectively learn the cycle structure information, and using higher‐order structural information—cycle information proves to significantly enhance the overall link prediction performance.

MosGraphGen: a novel tool to generate multi-omics signaling graphs to facilitate integrative and interpretable graph AI model development.

Multi-omics data, i.e., genomics, epigenomics, transcriptomics, proteomics, characterize cellular complex signaling systems from multi-level and multi-view and provide a holistic view of complex cellular signaling pathways. However, it remains challenging to integrate and interpret multi-omics data for mining key disease targets and signaling pathways. Graph AI models have been widely used to analyze graph-structure datasets, and are ideal for integrative multi-omics data analysis because they can naturally integrate and represent multi-omics data as a biologically meaningful multi-level signaling graph and interpret multi-omics data via graph node and edge ranking analysis. However, it is non-trivial for graph-AI model developers to pre-analyze multi-omics data and convert the data into biologically meaningful graphs, which can be directly fed into graph-AI models. To resolve this challenge, we developed mosGraphGen (multi-omics signaling graph generator), generating Multi-omics Signaling graphs (mos-graph) of individual samples by mapping multi-omics data onto a biologically meaningful multi-level background signaling network with data normalization by aggregating measurements and aligning to the reference genome. With mosGraphGen, AI model developers can directly apply and evaluate their models using these mos-graphs. In the results, mosGraphGen was used and illustrated using two widely used multi-omics datasets of TCGA and Alzheimer's disease (AD) samples. The code of mosGraphGen is open-source and publicly available via GitHub: https://github.com/FuhaiLiAiLab/mosGraphGen.

Node ranking algorithm using Graph Convolutional Networks and mini-batch training

This paper presents a novel algorithm for ranking nodes in graph-structured data using Graph Convolutional Networks (GCNs) combined with mini-batch training. The proposed method integrates local and global structural information, enabling a comprehensive understanding of node importance within complex networks. By employing a multi-layer GCN architecture with residual connections and dropout regularization, our approach captures intricate graph patterns while mitigating common issues such as vanishing gradients and overfitting. The node importance scores are computed using a Multi-Layer Perceptron (MLP), with the entire model trained using Mean Squared Error (MSE) loss optimized via the Adam algorithm. We demonstrate the scalability and effectiveness of our method through extensive experiments on various benchmark datasets, showcasing its superior performance in node ranking tasks compared to existing approaches.

Complex-Path: Effective and Efficient Node Ranking with Paths in Billion-Scale Heterogeneous Graphs

Node ranking in heterogeneous graphs, which quantifies the relative importance of nodes, can often be improved by incorporating information from relevant paths. Graph database and heterogeneous graph neural network (HGNN) are two main approaches to better solve this problem. Graph databases support efficient path queries for flexible path types but require manual design to combine results for node ranking. Conversely, current HGNNs can automatically integrate semantic information from multiple linear path types for accurate node ranking. However, our experiments show that they fail to outperform a multi-layer perceptron model that utilizes features extracted from multiple nonlinear conditional paths, which can be handled by graph databases. Therefore, we aim to enable HGNN to take advantage of these path types for better performance. However, HGNNs require a generalized path schema to define the structure of input paths, and incorporating each additional path type will significantly increase the required system memory and sampling time for HGNNs. To address these limitations, we introduce CompNode, a novel framework based on a new unified path schema definition called Complex-path, which is used to describe all the required path types, including nonlinear conditional path types. Then, we design a pre-aggregation method to reduce the required system memory and sampling time by pre-aggregating the same type of complex-path. Furthermore, we develop a model that combines semantic information from all aggregated complex-paths for accurate node ranking. Real-world experiments on identifying top potential high-value customers show CompNode outperforms state-of-the-art HGNNs by 20% in average precision and the previously deployed graph database method by 252% in success rate.

Time-dependent personalized PageRank for temporal networks: Discrete and continuous scales.

In this paper, we explore the PageRank of temporal networks (networks that evolve with time) with time-dependent personalization vectors. We consider both continuous and discrete time intervals and show that the PageRank of a continuous-temporal network can be nicely estimated by the PageRanks of the discrete-temporal networks arising after sampling. Additionally, precise boundaries are given for the estimated influence of the personalization vector on the ranking of a particular node. All ingredients in the classic PageRank definition, namely, the normalized matrix collecting the topology of the network, the damping factor, and the personalization vector are allowed, to the best of our knowledge, for the first time in the literature to vary independently with time. The theoretical results are illustrated by means of some real and synthetic examples.

New Random Walk Algorithm Based on Different Seed Nodes for Community Detection

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric (MC) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities.

Hybrid Tasmanian Devil and Elephant Herding Model-Based Optimal Cluster Head Selection and Routing in MANET

MANETs (Mobile AdHoc Networks) have major problems due to the resource-constrained nature of mobile nodes. MANET topology is highly uncertain due to the mobility of MANET nodes that affect the stability of interconnected links. This scenario results in an increased traffic overhead which affects the routing protocol performance and results in increased energy consumption. A routing scheme designed for MANET should be able to handle energy depletion issues and nodes’ mobility. This paper designs two novel schemes to enhance energy efficiency and network lifetime by performing clustering and routing in MANET. The Hybrid Tasmanian devil and Elephant herding optimization (HTDEHO) is used for clustering the MANET nodes to minimize the overhead, enhance the stability of the network topology, and reduce collision. The HTDEHO selects the optimal cluster head (CH) from a set of nodes based on their fitness value calculated by various parameters such as mobility-based node ranking, residual energy, distance, node degree, and optimal next hop CH selection. Dwarf mongoose optimization algorithm with Fuzzy variable (FDMO) algorithm selects optimal routing cost from CH to the base station based on various parameters such as throughput, delay, and distance. The efficiency of the proposed model is evaluated with different performance metrics such as energy consumption, throughput, end-to-end delay, and packet-dropping analysis. The performance of the proposed HTDEHO-FDMO classifier is compared with different techniques such as RDOAICRP, BFOA, MARP-HO, and FEKHO-QBA. Even after 170 iterations, the HTDEHO model retains a total of 10 alive nodes.

GraphADT: empowering interpretable predictions of acute dermal toxicity with multi-view graph pooling and structure remapping.

Accurate prediction of acute dermal toxicity (ADT) is essential for the safe and effective development of contact drugs. Currently, graph neural networks, a form of deep learning technology, accurately model the structure of compound molecules, enhancing predictions of their ADT. However, many existing methods emphasize atom-level information transfer and overlook crucial data conveyed by molecular bonds and their interrelationships. Additionally, these methods often generate "equal" node representations across the entire graph, failing to accentuate "important" substructures like functional groups, pharmacophores, and toxicophores, thereby reducing interpretability. We introduce a novel model, GraphADT, utilizing structure remapping and multi-view graph pooling (MVPool) technologies to accurately predict compound ADT. Initially, our model applies structure remapping to better delineate bonds, transforming "bonds" into new nodes and "bond-atom-bond" interactions into new edges, thereby reconstructing the compound molecular graph. Subsequently, we use MVPool to amalgamate data from various perspectives, minimizing biases inherent to single-view analyses. Following this, the model generates a robust node ranking collaboratively, emphasizing critical nodes or substructures to enhance model interpretability. Lastly, we apply a graph comparison learning strategy to train both the original and structure remapped molecular graphs, deriving the final molecular representation. Experimental results on public datasets indicate that the GraphADT model outperforms existing state-of-the-art models. The GraphADT model has been demonstrated to effectively predict compound ADT, offering potential guidance for the development of contact drugs and related treatments. Our code and data are accessible at: https://github.com/mxqmxqmxq/GraphADT.git.

Node2vec2rank: Large Scale and Stable Graph Differential Analysis via Multi-Layer Node Embeddings and Ranking.

Computational methods in biology can infer large molecular interaction networks from multiple data sources and at different resolutions, creating unprecedented opportunities to explore the mechanisms driving complex biological phenomena. Networks can be built to represent distinct conditions and compared to uncover graph-level differences-such as when comparing patterns of gene-gene interactions that change between biological states. Given the importance of the graph comparison problem, there is a clear and growing need for robust and scalable methods that can identify meaningful differences. We introduce node2vec2rank (n2v2r), a method for graph differential analysis that ranks nodes according to the disparities of their representations in joint latent embedding spaces. Improving upon previous bag-of-features approaches, we take advantage of recent advances in machine learning and statistics to compare graphs in higher-order structures and in a data-driven manner. Formulated as a multi-layer spectral embedding algorithm, n2v2r is computationally efficient, incorporates stability as a key feature, and can provably identify the correct ranking of differences between graphs in an overall procedure that adheres to veridical data science principles. By better adapting to the data, node2vec2rank clearly outperformed the commonly used node degree in finding complex differences in simulated data. In the real-world applications of breast cancer subtype characterization, analysis of cell cycle in single-cell data, and searching for sex differences in lung adenocarcinoma, node2vec2rank found meaningful biological differences enabling the hypothesis generation for therapeutic candidates. Software and analysis pipelines implementing n2v2r and used for the analyses presented here are publicly available.

Multi-view discriminative edge heterophily contrastive learning network for attributed graph anomaly detection

Attributed graph anomaly detection aims to identify abnormal nodes that significantly differ from most nodes in terms of their attribute or structure. Recent graph contrastive learning methods, which follow an augmenting-contrasting learning scheme, have shown promising results. However, these methods still have two key limitations. Firstly, the contrastive views generated through random perturbation may not conform to abnormal patterns. Secondly, the inability to effectively discriminate heterophilic edges in anomalous networks can adversely impact the detection performance. To this end, we propose a Multi-view discriminative Edge heterophiLy cOntrastive learning Network (MELON) for attributed graph anomaly detection. Our approach addresses the aforementioned limitations by integrating human knowledge of different anomaly patterns for data augmentation and designing an edge discriminator to identify edge homophily/heterophily in an unsupervised manner. In addition, a dual-channel encoder is also designed to capture representative representations of the nodes from the discriminated homophilic/heterophilic edges. We then use a decoder to reconstruct the original network from the node representations learned by the dual-channel encoder and rank nodes according to their reconstruction error as the anomaly metric. Extensive experiments on four public benchmark datasets demonstrate that our proposed method outperforms state-of-the-art baselines.

Vulnerability Assessment and Topology Reconstruction of Task Chains in UAV Networks

With the increasing complexity of environments and the diversity of task chains, individual unmanned aerial vehicles (UAVs) often struggle to satisfy the demands of task chains, including load capacity improvement, information perception, and information procession. In complex task chains involving various UAVs, such as area reconnaissance and fire rescue, any attack on critical UAVs can greatly disrupt the execution of the entire task chain by causing equipment damage or connectivity disruption. To ensure network resilience post attack, identifying vulnerable nodes in the UAV network becomes crucial. In this paper, a Vulnerability-based Topology Reconstruction Mechanism (VUTRM) is proposed to rank the importance of nodes in task chains and formulate a topology reconstruction. It consists of two parts: the first part is a Multi-metric Node Vulnerability Assessment Algorithm (MENVAL) used to rank the importance of nodes in task chains, and the second part is a Node Importance-based Topology Reconstruction Algorithm (NITRA) used to reconstruct the UAV network with the obtained node ranking. Finally, simulations carried out with simulation software demonstrate that our proposed method accurately identifies network vulnerabilities and promptly implements effective reconstruction measures to minimize network damage.

Epidemic Model-based Network Influential Node Ranking Methods: A Ranking Rationality Perspective

Existing surveys and reviews on Influential Node Ranking Methods (INRMs) have primarily focused on technical details, neglecting thorough research on verifying the actual influence of these nodes in a network. This oversight may result in erroneous rankings. In this survey, we address this gap by conducting an extensive analysis of 82 primary studies related to INRMs based on the epidemic model over the past 20 years. We statistically analyze and categorize benchmark networks into four types, and conclude that high-quality networks with complete information are insufficient and most INRMs only focus on undirected and unweighted networks, which encourages collaboration between industry and academia to provide optimized networks. Additionally, we categorize and discuss the strengths, weaknesses, and optimized crafts of seven categories of INRMs, helping engineers and researchers narrow down their choices when selecting appropriate INRMs for their specific needs. Furthermore, we define the Capability and Correctness metrics and utilize their usage frequency and functionality to assist engineers and researchers in prioritizing and selecting suitable metrics for different INRMs and networks. To our knowledge, this is the first survey that systematically summarizes the Capability and Correctness of INRMs, providing insights for the complex network community and aiding INRM selection and evaluation.

Improvement of Practical Byzantine Fault Tolerance Consensus Algorithm Based on DIANA in Intellectual Property Environment Transactions

In response to the shortcomings of the consensus algorithm for intellectual property transactions, such as high communication overhead, random primary node selection, and prolonged consensus time, a Practical Byzantine Fault Tolerance (PBFT) improvement algorithm based on Divisive Analysis (DIANA) D-PBFT algorithm is proposed. Firstly, the algorithm adopts the hierarchical clustering mechanism of DIANA to cluster nodes based on similarity, enhancing node partition accuracy and reducing the number of participating consensus nodes. Secondly, it designs a reward and punishment system based on node ranking, to achieve consistency between node status and permissions, timely evaluation, and feedback on node behaviours, thereby enhancing node enthusiasm. Then, the election method of the primary node is improved by constructing proxy and alternate nodes and adopting a majority voting strategy to achieve the selection and reliability of the primary node. Finally, the consistency protocol is optimised to perform consensus once within the cluster and once between all primary nodes, to ensure the accuracy of the consensus results. Experimental results demonstrate that the D-PBFT algorithm shows a better performance, in terms of communication complexity, throughput, and latency.

A protein network refinement method based on module discovery and biological information

BackgroundThe identification of essential proteins can help in understanding the minimum requirements for cell survival and development to discover drug targets and prevent disease. Nowadays, node ranking methods are a common way to identify essential proteins, but the poor data quality of the underlying PIN has somewhat hindered the identification accuracy of essential proteins for these methods in the PIN. Therefore, researchers constructed refinement networks by considering certain biological properties of interacting protein pairs to improve the performance of node ranking methods in the PIN. Studies show that proteins in a complex are more likely to be essential than proteins not present in the complex. However, the modularity is usually ignored for the refinement methods of the PINs.MethodsBased on this, we proposed a network refinement method based on module discovery and biological information. The idea is, first, to extract the maximal connected subgraph in the PIN, and to divide it into different modules by using Fast-unfolding algorithm; then, to detect critical modules according to the orthologous information, subcellular localization information and topology information within each module; finally, to construct a more refined network (CM-PIN) by using the identified critical modules.ResultsTo evaluate the effectiveness of the proposed method, we used 12 typical node ranking methods (LAC, DC, DMNC, NC, TP, LID, CC, BC, PR, LR, PeC, WDC) to compare the overall performance of the CM-PIN with those on the S-PIN, D-PIN and RD-PIN. The experimental results showed that the CM-PIN was optimal in terms of the identification number of essential proteins, precision-recall curve, Jackknifing method and other criteria, and can help to identify essential proteins more accurately.

Is 'distinctiveness centrality' actually distinctive? A comment on Fronzetti Colladon and Naldi (2020).

Distinctiveness centrality, which was proposed in 2020 to identify nodes that are connected to poorly-connected neighbors, is simply a minor variation on two existing centrality measures: beta centrality proposed in 1987, and gamma centrality proposed in 2011. In toy, empirical, and generated networks, I show that these three centrality measures yield identical node rankings under nearly all circumstances. Researchers seeking to identify nodes that are connected to poorly-connected others should not use distinctiveness centrality, and instead should use either beta or gamma centrality because they are more widely-known in the literature, are more flexible, and are computationally simpler. Additionally, researchers should be cautious when proposing new centrality measures, taking care to avoid duplicating measures that already exist.

Efficient Optimization approach in WSN using Multicast Forwarding Scheme in 6LowPAN Environment

The rapidly growing network of devices that are connected known as the Internet of Things, also referred to as IoT, is designed to collect and exchange data. These devices are integrated with sensors, software, and other technologies. An IPv6-based routing system called 6LowPAN was created especially for Internet of Things devices with little resources. However, because multicast packets must be replicated to every multicast group member, the conventional multicast forwarding technique in 6LowPAN may be wasteful. This can result in excessive energy usage and network traffic, particularly in large-scale Internet of Things implementations. An optimization process is presented here using a multicast forwarding scheme. In the proposed forwarding scheme, nodes can send multicast packets up and down at Low Power and Lossy networks over the 6LowPAN environment. Should the sink node be on the root node, it should immediately request that other nodes join the multicast messaging network of things. If otherwise, an ICMPv6 packet will be sent towards the root node in the Destination-oriented Directed-Acyclic Graphs (DODAG) tree, which expands the multicast messages in the first source's interest. In multi-bounce forward straight-line topology, when the DODAG network root is the source of multicast congestion, it exhibits a similar ratio of packet delivery and delay from end to end with a minimal memory overhead. When traffic via multicast originates from the most important rank node in a backward straight-line topology, this paper focuses on the efficiency of the multicast network at 6LowPAN.

Status-Aware Signed Heterogeneous Network Embedding With Graph Neural Networks.

Many real-world applications are inherently modeled as signed heterogeneous networks or graphs with positive and negative links. Signed graph embedding embeds rich structural and semantic information of a signed graph into low-dimensional node representations. Existing methods usually exploit social structural balance theory to capture the semantics of the complex structure in a signed graph. These methods either omit the node features or may discard the direction information of the links. To address these issues, we propose a new framework, called a status-aware graph neural network (S-GNN), to boost the representation learning performance. S-GNN is equipped with a loss function designed based on status theory, a social-psychological theory specifically developed for directed signed graphs. Extensive experimental results on benchmarking datasets verified that S-GNN can distill comprehensive information ingrained in a signed graph in the embedding space. Specifically, S-GNN achieves state-of-the-art accuracy, robustness, and scalability: it speeds up the processing time of link sign prediction by up to 6.5 × and increases accuracy by up to 18.8% as compared with the alternatives. We also show that S-GNN can obtain effective status scores of nodes for link sign prediction and node ranking tasks, both of which yield state-of-the-art performance.

Dynamic identification of important nodes in complex networks based on the KPDN–INCC method

This article focuses on the cascading failure problem and node importance evaluation method in complex networks. To address the issue of identifying important nodes in dynamic networks, the method used in static networks is introduced and the necessity of re-evaluating node status during node removal is proposed. Studies have found that the methods for identifying dynamic and static network nodes are two different directions, and most literature only uses dynamic methods to verify static methods. Therefore, it is necessary to find suitable node evaluation methods for dynamic networks. Based on this, this article proposes a method that integrates local and global correlation properties. In terms of global features, we introduce an improved k-shell method with fusion degree to improve the resolution of node ranking. In terms of local features, we introduce Solton factor and structure hole factor improved by INCC (improved network constraint coefficient), which effectively improves the algorithm’s ability to identify the relationship between adjacent nodes. Through comparison with existing methods, it is found that the KPDN–INCC method proposed in this paper complements the KPDN method and can accurately identify important nodes, thereby helping to quickly disintegrate the network. Finally, the effectiveness of the proposed method in identifying important nodes in a small-world network with a random parameter less than 0.4 was verified through artificial network experiments.

Leverage Centrality on Barycentric Subdivision of Some Graphs

The centrality index on a graph is a real-valued function on the nodes, which provides a ranking of vital nodes in the graph. Each node could be important from an angle, depending on how the concept of importance is defined. There are various measures of centrality, and each one defines a node's importance from a different perspective and provides relevant analytical information about the graph. Leverage centrality of nodes in a graph was defined by Joyce et al. in 2010 as a means to analyze connections within the brain. The definition of this measure shows that it is unique among existing measures in that it counts not just a node's degree, but also its neighbor's degrees. In this paper, we study the leverage centrality of nodes in the $k^{th}$ barycentric subdivision of some classes of graphs. This is a new concept in literature. The process can make regular graphs irregular, and the leverage center of the edge-subdivided graphs under study was investigated.