Top-k Nodes Research Articles

Identifying influential nodes in social networks via improved Laplacian centrality

Identifying influential nodes in social networks has significant applications in terms of social analysis and information dissemination. How to capture the crucial features of influential nodes without increasing the computational complexity is an urgent issue to be solved in the context of big data. Laplacian centrality (LC) measures nodal influence by computing nodes' degree, making it extremely low complexity. However, there is still significant room for improvement. Consequently, we propose the improved Laplacian centrality (ILC) to identify influential nodes based on the concept of self-consistent. Identifying results on 9 real networks prove that ILC is superior to LC and other 6 classical measures in terms of ranking accuracy, top-k nodes identification and discrimination capability. Moreover, the computational complexity of ILC has not significantly increased compared to LC, and remains the linear order of magnitude O(m). Additionally, ILC has excellent robustness and universality such that there is no need to adjust parameters according to different network structures.

MHPD: An efficient evaluation method for influence maximization on hypergraphs

Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top-K nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely 0.25 % compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains 98.81 % of the solution accuracy while requiring only 0.11 % of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of 23.4 % over the best baseline algorithm.

Influence Maximization Based on Adaptive Graph Convolution Neural Network in Social Networks

The influence maximization problem is a hot issue in the research on social networks due to its wide application. The problem aims to find a small subset of influential nodes to maximize the influence spread. To tackle the challenge of striking a balance between efficiency and effectiveness in traditional influence maximization algorithms, deep learning-based influence maximization algorithms have been introduced and have achieved advancement. However, these algorithms still encounter two key problems: (1) Traditional deep learning models are not well-equipped to capture the latent topological information of networks with varying sizes and structures. (2) Many deep learning-based methods use the influence spread of individual nodes as labels to train a model, which can result in an overlap of influence among the seed nodes selected by the model. In this paper, we reframe the influence maximization problem as a regression task and introduce an innovative approach to influence maximization. The method adopts an adaptive graph convolution neural network which can explore the latent topology information of the network and can greatly improve the performance of the algorithm. In our approach, firstly, we integrate several network-level attributes and some centrality metrics into a vector as the presentation vector of nodes in the social network. Next, we propose a new label generation method to measure the influence of nodes by neighborhood discount strategy, which takes full account of the influence overlapping problem. Subsequently, labels and presentation vectors are fed into an adaptive graph convolution neural network model. Finally, we use the well-trained model to predict the importance of nodes and select top-K nodes as a seed set. Abundant experiments conducted on various real-world datasets have confirmed that the performance of our proposed algorithm surpasses that of several current state-of-the-art algorithms.

Identifying key spreaders in complex networks based on local clustering coefficient and structural hole information

Identifying key spreaders in a network is one of the fundamental problems in the field of complex network research, and accurately identifying influential propagators in a network holds significant practical implications. In recent years, numerous effective methods have been proposed and widely applied. However, many of these methods still have certain limitations. For instance, some methods rely solely on the global position information of nodes to assess their propagation influence, disregarding local node information. Additionally, certain methods do not consider clustering coefficients, which are essential attributes of nodes. Inspired by the quality formula, this paper introduces a method called Structural Neighborhood Centrality (SNC) that takes into account the neighborhood information of nodes. SNC measures the propagation power of nodes based on first and second-order neighborhood degrees, local clustering coefficients, structural hole constraints, and other information, resulting in higher accuracy. A series of pertinent experiments conducted on 12 real-world datasets demonstrate that, in terms of accuracy, SNC outperforms methods like CycleRatio and KSGC. Additionally, SNC demonstrates heightened monotonicity, enabling it to distinguish subtle differences between nodes. Furthermore, when it comes to identifying the most influential Top-k nodes, SNC also displays superior capabilities compared to the aforementioned methods. Finally, we conduct a detailed analysis of SNC and discuss its advantages and limitations.

On exploring node-feature and graph-structure diversities for node drop graph pooling

Graph Neural Networks (GNNs) have been successfully applied to graph-level tasks in various fields such as biology, social networks, computer vision, and natural language processing. For the graph-level representations learning of GNNs, graph pooling plays an essential role. Among many pooling techniques, node drop pooling has garnered significant attention and is considered as a leading approach. However, existing node drop pooling methods, which typically retain the top-k nodes based on their significance scores, often overlook the diversity inherent in node features and graph structures. This limitation leads to suboptimal graph-level representations. To overcome this, we introduce a groundbreaking plug-and-play score scheme, termed MID. MID comprises a Multidimensional score space and two key operations: flIpscore and Dropscore. The multidimensional score space depicts the significance of nodes by multiple criteria; the flipscore process promotes the preservation of distinct node features; the dropscore compels the model to take into account a range of graph structures rather than focusing on local structures. To evaluate the effectiveness of our proposed MID, we have conducted extensive experiments by integrating it with a broad range of recent node drop pooling methods, such as TopKPool, SAGPool, GSAPool, and ASAP. In particular, MID has proven to bring a significant average improvement of approximately 2.8% over the four aforementioned methods when tested on 17 real-world graph classification datasets. Code is available at https://github.com/whuchuang/mid.

Multi-View Graph Convolutional Networks with Differentiable Node Selection

Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in the real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this article, we apply Graph Convolutional Network (GCN) to cope with heterogeneous graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top- k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module, and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks, and the experimental results indicate that MGCN-DNS achieves pleasurable performance on several benchmark multi-view datasets.

EARLY: Efficient and Reliable Graph Neural Network for Dynamic Graphs

Graph neural networks have been widely used to learn node representations for many real-world static graphs. In general, they learn node representations by recursively aggregating information from neighbors. However, graphs in many applications are dynamic, evolving with continuous graph events, such as node feature and graph structure updates. These events require the node representations to be updated accordingly. Currently, due to the real-time requirement, how to efficiently and reliably update node representations under continuous graph events is still an open problem. Recent studies propose two solutions to partially address this problem, but their performance is still limited. First, local-based GNNs only update the nodes directly involved in events, suffering from the quality-deficit issue, since they neglect the other nodes affected by these events. Second, neighbor-sampling GNNs propose to sample neighbors to accelerate neighbor aggregation computations, encountering the neighbor-redundant issue. These sampled neighbors may be similar and cannot reflect the distribution of all neighbors, leading that node representations aggregated on these redundant neighbors may differ from those aggregated on all neighbors. In this paper, we propose an efficient and reliable graph neural network, namely EARLY, to update node representations for dynamic graphs. We first identify the top-k influential nodes that are most affected by graph events. Then, to sample neighbors diversely, we propose a diversity-aware layer-wise sampling technique. We theoretically demonstrate that this technique can decrease the sampling expectation error and learn more reliable node representations. Therefore, the top-k nodes selection and diversity-aware sampling enable EARLY to efficiently update node representations in a reliable way. Extensive experiments on the five real-world graphs demonstrate the effectiveness and efficiency of our proposed EARLY.

A novel algorithm for identifying influential nodes in complex networks based on local propagation probability model

Identifying influential nodes in complex networks is an essential research issue in network science since it may attribute to understand network structure and function. Majority of existing methods have been established by considering topological characteristics of networks. In this paper, we put forward a novel algorithm based on the Local Propagation Probability (LPP) model for identifying influential nodes in complex networks. The core idea of LPP algorithm is that the nodal influence is measured by total comprehensive scores of neighbor nodes within its three level neighborhood. Specially, the comprehensive score is calculated from three dimensions, namely the propagation influence score between different order neighbors, the propagation influence score in the same order neighbors and the hierarchical structure information of nodes. To validate the performance and applicability of the proposed algorithm, LPP is compared with eight state-of-the-art and competitive algorithms on nine real-world networks. Experimental results demonstrate that LPP performs better in terms of ranking accuracy, effectiveness, top-k nodes and distinguishing ability. The low time complexity allows LPP to be applied to large-scale sparse networks.

Unsupervised Learning-based New Seed-Expanding Approach using Influential Nodes for Community Detection in Social Networks

Several recent studies focus on community structure due to its importance in analyzing and understanding complex networks. Communities are groups of nodes highly connected with themselves and not much connected to the rest of the network. Community detection helps us to understand the properties of the dynamic process within a network. In this paper, we propose a novel seed-centric approach based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and k-means algorithm to find communities in a social network. TOPSIS is used to find the seeds within this network using the benefits of multiple measure centralities. The use of a single centrality to determine seeds within a network, like in classical algorithms of community detection, doesn’t succeed in the majority of cases to reach the best selection of seeds. Therefore, we consider all centrality metrics as a multi-attribute of TOPSIS and we rank nodes based on the TOPSIS’ relative closeness. The Top-K nodes extracted from TOPSIS will be considered as seeds in the proposed approach. Afterwards, we apply the k-means algorithm using these seeds as starting centroids to detect and construct communities within a social network. The proposed approach is tested on Facebook ego network and validated on the famous dataset having the ground-truth community structure Zachary karate club. Experimental results on Facebook ego network show that the dynamic k-means provides reasonable communities in terms of distribution of nodes. These results are confirmed using Zachary karate club. Two detected communities are detected with higher normalized mutual information NMI and Adjusted Rand Index ARI compared to other seed centric algorithms such as Yasca, LICOD, etc. The proposed method is effective, feasible, and provides better results than other available state-of-the-art community detection algorithms.

Ranking influential spreaders based on both node k-shell and structural hole

The ranking of individual spreaders aims to measure the influential capability of individual nodes and is important to control information spreading in a network. However, many ranking methods are either degree-based, k-shell-related or a combination of the two, which are not necessarily related to influential capability. Inspired by the strengths of the k-shell decomposition method, this work improves it on the basis of structural holes (SH) and proposes a novel ranking method, SHKS. Different from the efforts that aim only to improve the k-shell decomposition method, this work considers the k-shell and SH-based centrality of a node as well as its neighbors and second-order neighbors. Based on the flexible combination of k-shell and SH, SHKS can identify not only the core nodes with large k-shell indices but also the nodes that have small k-shell indices but play an important role in bridging different parts of a network. Experimental results show that SHKS presents better performance than baseline methods in terms of the Kendall τ correlation results, and the average improvements range from 1.3% to 121.1%. SHKS also has the best monotonicity, and its average monotonicity value on experimental networks is close to 0.99. Moreover, SHKS has good performance in identifying the most influential top-k nodes compared with baseline methods.

The manifold regularized SVDD for noisy label detection

Supervised Learning (SL) celebrates a lot of research topics in machine learning (ML) and provides a large number of applications in multimedia. The effectiveness and performance of supervised learning are highly dependent on the quality of labeled samples, and poor or mislabeled labels always damage pre-knowledge and produce disastrous results. One of the notable works is the development of a model for detecting noisy labels in large-scale data sets for supervised classification. This paper introduces a new method for noisy label detection that combines the support vector data description (SVDD) model with manifold regularization. The proposed method is able to detect the noisy label in the testing set. In addition, we adopt K nearest neighbors to obtain the K-nearest neighbor graph, and the k-core algorithm is used to select noise nodes by selecting the influential nodes with larger k values in the K-NN graph. Experimental results over UCI data sets show that the manifold regularized SVDD can effectively detect the noise labels data, and presents better performance over most methods in terms of the outlier detection accuracy, and the average accuracy is mostly above 50%, even 100%. Moreover, manifold regularized SVDD has good performance in detecting the most influential top-k nodes compared with other methods.

Hierarchical Structure-Feature Aware Graph Neural Network for Node Classification

In recent years, graph neural network is used to process graph data and has been successfully applied to graph node classification task. Due to the complexity of graph structure and the difficulty of obtaining node labels, node classification in datasets with fewer labels becomes a challenge. Existing node classification problems with few-label nodes datasets usually use neighbor aggregation schemes. However, these methods lack the “graph pooling mechanism,” which makes these models impossible to make full use of the global graph information. To solve the problem, we propose a Hierarchical Structure-Feature aware Graph Neural Network (HSFGNN) model. The model learns node features by a hierarchical mechanism that repeatedly utilizes coarsening and refining methods at different levels. Firstly, we use topological information, node characteristics and connectivity of the graph to construct an intuitive and effective coarsening part based on multivariable analysis technology. Secondly, we aggregate the unselected nodes’ features into the top-k nodes, so that the coarser nodes contain more abundant valid graph information. Finally, we propose an additional attention mechanism to obtain more accurate final representations of nodes. Experimental results show that the HSFGNN model achieves outstanding classification accuracy on the dataset with less labeled data.

Influence Maximization Based on Backward Reasoning in Online Social Networks

Along with the rapid development of information technology, online social networks have become more and more popular, which has greatly changed the way of information diffusion. Influence maximization is one of the hot research issues in online social network analysis. It refers to mining the most influential top-K nodes from an online social network to maximize the final propagation of influence in the network. The existing studies have shown that the greedy algorithms can obtain a highly accurate result, but its calculation is time-consuming. Although heuristic algorithms can improve efficiency, it is at the expense of accuracy. To balance the contradiction between calculation accuracy and efficiency, we propose a new framework based on backward reasoning called Influence Maximization Based on Backward Reasoning. This new framework uses the maximum influence area in the network to reversely infer the most likely seed nodes, which is based on maximum likelihood estimation. The scheme we adopted demonstrates four strengths. First, it achieves a balance between the accuracy of the result and efficiency. Second, it defines the influence cardinality of the node based on the information diffusion process and the network topology structure, which guarantees the accuracy of the algorithm. Third, the calculation method based on message-passing greatly reduces the computational complexity. More importantly, we applied the proposed framework to different types of real online social network datasets and conducted a series of experiments with different specifications and settings to verify the advantages of the algorithm. The results of the experiments are very promising.

ABCDE: Approximating Betweenness-Centrality ranking with progressive-DropEdge.

Betweenness-centrality is a popular measure in network analysis that aims to describe the importance of nodes in a graph. It accounts for the fraction of shortest paths passing through that node and is a key measure in many applications including community detection and network dismantling. The computation of betweenness-centrality for each node in a graph requires an excessive amount of computing power, especially for large graphs. On the other hand, in many applications, the main interest lies in finding the top-k most important nodes in the graph. Therefore, several approximation algorithms were proposed to solve the problem faster. Some recent approaches propose to use shallow graph convolutional networks to approximate the top-k nodes with the highest betweenness-centrality scores. This work presents a deep graph convolutional neural network that outputs a rank score for each node in a given graph. With careful optimization and regularization tricks, including an extended version of DropEdge which is named Progressive-DropEdge, the system achieves better results than the current approaches. Experiments on both real-world and synthetic datasets show that the presented algorithm is an order of magnitude faster in inference and requires several times fewer resources and time to train.

Identifying and ranking super spreaders in real world complex networks without influence overlap

In the present-days complex networks modeled on real-world data contain millions of nodes and billions of links. Identifying super spreaders in such an extensive network is a challenging task. Super spreaders are the most important or influential nodes in the network that play the central role during an infection spreading or information diffusion process. Depending on the application, either the most influential node needs to be identified, or a set of initial seed nodes are identified that can maximize the collective influence or the total spread in the network. Many centrality measures have been proposed to rank nodes in a complex network such as ‘degree’, ‘closeness’, ‘betweenness’, ‘coreness’ or ‘k-shell’ centrality, among others. All have some kind of inherent limitations. Mixed degree decomposition or m-shell is an improvement over k-shell that yields better ranking. Many researchers have employed single node identification heuristics to select multiple seed nodes by considering top-k nodes from the ranked list. This approach does not results in the optimal seed nodeset due to the considerable overlap in total spreading influence. Influence overlap occurs when multiple nodes from the seed nodeset influence a specific node, and it is counted multiple times during total collective influence computation. In this paper, we exploit the ‘node degree’, ‘closeness’ and ‘coreness’ among the nodes and propose novel heuristic template to rank the super spreaders in a network. We employ k-shell and m-shell as a coreness measure in two variants for a comparative evaluation. We use a geodesic-based constraint (enforcing a minimum distance between seed nodes) to select an initial seed nodeset from that ranked nodes for influence maximization instead of selecting the top-k nodes naively. All models and metrics are updated to avoid overlapping influence during total spread computation. Experimental simulation with the SIR (Susceptible-Infectious-Recovered) spreading model and an evaluation with performance metrics like spreadability, monotonicity of ranking, Kendall’s rank correlation on some benchmark real-world networks establish the superiority of the proposed methods and the improved seed node selection technique.

Finding Top-k Nodes for Temporal Closeness in Large Temporal Graphs

The harmonic closeness centrality measure associates, to each node of a graph, the average of the inverse of its distances from all the other nodes (by assuming that unreachable nodes are at infinite distance). This notion has been adapted to temporal graphs (that is, graphs in which edges can appear and disappear during time) and in this paper we address the question of finding the top-k nodes for this metric. Computing the temporal closeness for one node can be done in O(m) time, where m is the number of temporal edges. Therefore computing exactly the closeness for all nodes, in order to find the ones with top closeness, would require O(nm) time, where n is the number of nodes. This time complexity is intractable for large temporal graphs. Instead, we show how this measure can be efficiently approximated by using a “backward” temporal breadth-first search algorithm and a classical sampling technique. Our experimental results show that the approximation is excellent for nodes with high closeness, allowing us to detect them in practice in a fraction of the time needed for computing the exact closeness of all nodes. We validate our approach with an extensive set of experiments.

Efficient Algorithms for Approximate Single-Source Personalized PageRank Queries

Given a graph G , a source node s, and a target node t , the personalized PageRank ( PPR ) of t with respect to s is the probability that a random walk starting from s terminates at t . An important variant of the PPR query is single-source PPR ( SSPPR ), which enumerates all nodes in G and returns the top- k nodes with the highest PPR values with respect to a given source s . PPR in general and SSPPR in particular have important applications in web search and social networks, e.g., in Twitter’s Who-To-Follow recommendation service. However, PPR computation is known to be expensive on large graphs and resistant to indexing. Consequently, previous solutions either use heuristics, which do not guarantee result quality, or rely on the strong computing power of modern data centers, which is costly. Motivated by this, we propose effective index-free and index-based algorithms for approximate PPR processing, with rigorous guarantees on result quality. We first present FORA, an approximate SSPPR solution that combines two existing methods—Forward Push (which is fast but does not guarantee quality) and Monte Carlo Random Walk (accurate but slow)—in a simple and yet non-trivial way, leading to both high accuracy and efficiency. Further, FORA includes a simple and effective indexing scheme, as well as a module for top- k selection with high pruning power. Extensive experiments demonstrate that the proposed solutions are orders of magnitude more efficient than their respective competitors. Notably, on a billion-edge Twitter dataset, FORA answers a top-500 approximate SSPPR query within 1s, using a single commodity server.

Fast top-k similarity search in large dynamic attributed networks

In this paper, we study the problem of retrieving top-k nodes that are similar to a given query node in large dynamic attributed networks. To tackle this problem, we propose a fast Attribute augmented Single-source Path similarity algorithm (ASP). Our ASP constructs an attribute augmented network that integrates both node structure and attribute similarities through similarity scores computed by an efficient single-source path sampling scheme. It also contains simple and effective updating schemes to maintain similarity scores for dynamic edge insertions and deletions. We provide an upper bound of the sampling size of ASP for obtaining an ϵ-approximation estimation of similarity scores with probability at least 1−δ. We theoretically prove that the sampling size and computational complexity of ASP are significantly lower than that of deploying the currently known most effective method Panther. Implementation results from extensive experiments in both synthetic networks and real-world social networks show that our ASP achieves better convergence performance, runs faster than the baselines, and effectively captures both structure and attribute similarities of the nodes. Specifically, we show that our algorithm can return top-k similar nodes for any query node in the real-world network at least 44x faster than the state-of-the-art methods, and update similarity scores in about 1 second for a batch of network modifications in a network of size 1,000,000.

Resampling-based predictive simulation framework of stochastic diffusion model for identifying top-K influential nodes

We address a problem of efficiently estimating the influence of a node in information diffusion over a social network. Since the information diffusion is a stochastic process, the influence degree of a node is quantified by the expectation, which is usually obtained by very time-consuming many runs of simulation. Our contribution is that we proposed a framework for predictive simulation based on the leave-N-out cross-validation technique that well approximates the error from the unknown ground truth for two target problems: one to estimate the influence degree of each node, and the other to identify top-K influential nodes. The method we proposed for the first problem estimates the approximation error of the influence degree of each node, and the method for the second problem estimates the precision of the derived top-K nodes, both without knowing the true influence degree. We experimentally evaluate the proposed methods using the three real-world networks and show that they can serve as a good measure to solve the target problems with far fewer runs of simulation ensuring the accuracy when the leave-half-out cross-validation, i.e., N is the half of the number of runs, is used, which means that one can identify the influential nodes without knowing exactly their influence degree in good accuracy.

Identifying Top- k Nodes in Social Networks

Top- k nodes are the important actors for a subjectively determined topic in a social network. To some extent, a topic is taken as a ranking criteria for identifying top- k nodes. Within a viral marketing network, subjectively selected topics can include the following: Who can promote a new product to the largest number of people, and who are the highest spending customers? Based on these questions, there has been a growing interest in top- k nodes research to effectively identify key players. In this article, we review and classify existing literature on top- k nodes identification into two major categories: top- k influential nodes and top- k significant nodes. We survey both theoretical and applied work in the field and describe promising research directions based on our review. This research area has proven to be beneficial for data analysis on online social networks as well as practical applications on real-life networks.