A Review on Methods to Identify Influential Nodes in Complex Networks

Influential nodes refer to the ability of a node to spread information in complex networks. Identifying influential nodes is an important problem in complex networks which plays a key role in many applications such as rumor controlling, virus spreading, viral market advertising, research paper views, and citations. Basic measures like degree centrality, betweenness centrality, closeness centrality are identifying influential nodes but they are incapable of largescale networks due to time complexity issues. Chen et al. [1] proposed semi-local centrality, which is reducing computation complexity and finding influential nodes in the network. Recently Yang et al. 2020 [2] proposed a novel centrality measure based on degree and clustering coefficient for identifying the influential nodes. Sanjay et al. 2020 [3] gave voterank and neighborhood coreness-based algorithms for finding the influenced nodes in the network. Zhiwei et al. 2019 [4] considered the average shortest path to discover the influenced node in the network. These are the few recent local,global and mixed centralities. In this paper, we show a broad view of recent methods for finding influential nodes in complex networks. It also analyzes the new challenges and limitations for a better understanding of each method in detail. The experimental results based on these methods show better performance compared with existing basic centrality measures.

The issue of mining influential nodes in complex networks is a topic of immense interest. Recently, many methods have been proposed, but they suffer from certain limitations. In this article, a novel centrality measure based on local fuzzy information centrality (LFIC) is proposed. LFIC puts forward the concept that the inner structure of a node’s box contains information about the node’s importance. LFIC uses the amount of information contained in the node’s box as a measure of its importance. In LFIC, the uncertainty of information contained in nodes’ boxes is measured by the improved Shannon entropy. Most importantly, fuzzy logic is applied to deal with the uncertainty of neighbor nodes’ contributions to the center node’s importance, which is neglected by most existing methods. To verify the effectiveness of our proposed method, six existing methods are used for comparison and five experiments are conducted using six real-world complex networks. The experimental results indicate that the influential nodes identified by LFIC can cause a wider scope of infection in networks and have a larger effect on the network connectivity, thereby proving the effectiveness and accuracy of LFIC. The correlation between nodes’ LFIC values and their real infection ability is highly positive according to Kendall’s tau coefficient, proving LFIC’s credibility and superiority. The extension of LFIC, namely the bi-directional local fuzzy information centrality, is also proposed to explore its feasibility in weighted directed complex networks.

A novel potential edge weight method for identifying influential nodes in complex networks based on neighborhood and position

Efficiently identifying multiple influential nodes is crucial for maximizing information diffusion and minimizing rumor spread in complex networks. Selecting multiple influential seed nodes requires consideration of both their individual influence potential and their spatial dispersion within the network topology to avoid overlapping propagation ranges ("rich-club effect"). Traditional VoteRank method suffer from two key limitations: (1) they assume uniform voting contributions from a node to all its neighbors, neglecting the impact of topological similarity (structural homophily) on voting preferences observed in real-world scenarios, and (2) they employ a homogeneous voting attenuation strategy which inadequately suppresses the propagation range overlap among selected seed nodes. To address these shortcomings, this paper proposes IMVoteRank, an improved VoteRank algorithm featuring dual innovations. First, we introduce a Structural Similarity-Driven Voting Contribution Mechanism. Recognizing that voters (nodes) are more likely to support candidates (neighbors) with whom they share stronger topological ties, we decompose a neighbor's voting contribution into two components: a Direct Connection Contribution and a Structural Similarity Contribution (quantified using common neighbors). A dynamic weight parameter θ, adjusted based on the candidate node's degree, balances these components, significantly refining vote allocation accuracy. Second, we devise a Dynamic Group Isolation Strategy. During each iteration, after selecting the highest-scoring seed node <i>v<sub>max</sub></i>, we identify and isolate a tightly-knit group (OG) centered around it. This involves: (i) forming an initial group based on shared neighbor density with <i>v<sub>max</sub></i>, (ii) expanding it by incorporating nodes with more connections inside the group than outside, and (iii) isolating this group by setting the voting capacity (Va) of all its members to zero and virtually removing their connections from the adjacency matrix. Neighbors of <i>v<sub>max</sub></i> not in OG have their <i>Va</i> halved. This strategy proactively enforces spatial dispersion among seeds. Extensive simulations using the Susceptible-Infected-Recovered (SIR) propagation model on nine diverse real-world networks (ECON-WM3, Facebook-SZ, USAir, Celegans, ASOIAF, Dnc-corecipient, ERIS1176, DNC-emails, Facebook-combined) demonstrate the superior performance of IMVoteRank. Compared to seven benchmark methods (Degree, K-shell, VoteRank, NCVoteRank, VoteRank++, AIGCrank, EWV), IMVoteRank consistently achieves significantly larger final propagation coverage (infected scale) for a given number of seed nodes and transmission probability (<i>β</i>=0.1). Furthermore, seeds selected by IMVoteRank exhibit a consistently larger average shortest path length (<i>Ls</i>) among themselves across most networks, confirming their effective topological dispersion. This combination of high individual influence potential (optimized voting) and low redundancy (group isolation) directly translates to more efficient global information spread, as evidenced by the SIR results. Tests on LFR benchmark networks further validate these advantages, particularly at transmission rates above the epidemic threshold. IMVoteRank effectively overcomes the limitations of traditional voting models by integrating structural similarity into the voting process and employing dynamic group isolation to ensure seed dispersion. It provides a highly effective and physically well-grounded approach for identifying multiple influential nodes in complex networks, optimizing the trade-off between influence strength and spatial coverage. Future work will focus on enhancing computational efficiency for large-scale networks and exploring the impact of meso-scale community structures.

Ranking influential nodes in complex network using edge weight degree based shell decomposition

Identifying influential nodes in complex networks: Effective distance gravity model

Identifying influential nodes in complex networks is crucial for applications like information diffusion, rumor propagation, and epidemic spreading. Existing methods often assume uniform importance among neighbor nodes or fail to account for the structural and semantic diversity of relationships in heterogeneous networks. This leads to suboptimal identification of influential nodes, particularly in complex, attribute-rich networks. To address these shortcomings, a meta-path embedding-based graph attention network model is proposed, namely MEGA. MEGA is utilized to identify influential nodes in heterogeneous networks. This paper attempts to identify the influential set of author nodes in academic networks, defined as the set of nodes whose influence maximizes the spread of information. MEGA is described as follows. Firstly, the required meta-paths are defined, and node embeddings are obtained using a meta-path embedding method. Then, the subgraph networks corresponding to each meta-path network are generated based on random walks. Further, the graph attention network is employed to assign different weight values to neighbor nodes within the subgraph networks, indicating the varying influence of nodes on their neighbor nodes. Finally, the influence of nodes in the subgraph network is calculated using entropy, and the influence values from all subgraphs are aggregated to obtain the final influence value of each node. The effectiveness of MEGA is validated using analysis metrics from the independent cascade model. Experimental results demonstrate MEGA exceeds six baseline methods in terms of the influence spread across three datasets.

The identification of influential nodes in complex networks is a hot topic among scholars. Classical methods commonly analyze single node information or static structures but seldom emphasize dynamic properties and the interactive influence of nodes. Here, we proposed an improved Dynamic-Sensitive centrality (IDS) method by considering the interactive influence of both the self and neighbor nodes. Based on six real aviation networks and the Susceptible Infected Recovered (SIR) spreading disease model, we simulated the actual spreading process within these networks. Relevant experiments were conducted through Kendall’s correlation coefficient, the imprecision function, and the complementary cumulative distribution function. The experimental results demonstrated that the IDS can more accurately identify the influential node and effectively differentiate the node influence in the network compared with other benchmark methods. Especially in the EU air-2 network, the IDS results in Kendall’s correlation coefficient are improved by 105% compared to the DS centrality.

Abstract. Connecting points of interest through a well-planned, inter-connected network provides manifold benefits to commuters and service providers. In the South African context, traffic congestion has become of great concern. Given how the South Africa community is slowly developing towards the use of multi-modes of mobility, the Gautrain network can be used to promote the use of multi-modes of mobility, as the Gautrain has been identified as the backbone of mobility within the Gauteng province. Currently commuters have the option to board the Gaubus (a form of Bus Rapid Transit) at their origin points which will take them to the Gautrain station to board the Gautrain. The problem to be solved arises when a commuter wishes to traverse from any bus stop to the Gautrain station, currently he/she only has one option and if the bus network has a shutdown at any point in the network the commuter’s journey will not be possible. In solving this problem, we consider the problem of graph robustness (that is creating new alternative routes to increase node/bus stop connectivity). We initial use Strava data, to identify locations were cyclist prefer to cycle and at what time of day. In graph theory, the nodes with most spreading ability are called influential nodes. Identification of most influential nodes and ranking them based on their spreading ability is of vital importance. Closeness centrality and betweenness are one of the most commonly used methods to identify influential nodes in complex networks. Using the Gaubus network we identify the influential nodes/ bus stops, using the betweenness centrality measure. The results reveal the influential nodes with the highest connectivity as these have cross-connections in the network. Identification of the influential nodes presents an important implication for future planning, accessibility, and, more generally, quality of life.

Identifying influential nodes in complex networks is essential for network robust and stability, such as viral marketing and information control. Various methods have been proposed to define the influence of nodes. In this paper, we comprehensively consider the global position and local structure to identify influential nodes. The number of iterations in the process of k-shell decomposition is taken into consideration, and the improved k-shell decomposition is then put forward. The improved k-shell decomposition and degree of target node are taken as the benchmark centrality, in addition, as is well known, the effect between node pairs is inversely proportional to the shortest path length between two nodes, and then we also consider the effect of neighbors on target node. To evaluate the performance of the proposed method, susceptible-infected (SI) model is adopted to simulate the spreading process in four real networks, and the experimental results show that the proposed method has obvious advantages over classical centrality measures in identifying influential nodes.

Identifying influential nodes in complex networks is of both theoretical and practical importance. Existing methods identify influential nodes based on their positions in the network and assume that the nodes are homogeneous. However, node heterogeneity (i.e., different attributes such as interest, energy, age, and so on) ubiquitously exists and needs to be taken into consideration. In this paper, we conduct an investigation into node attributes and propose a graph signal processing based centrality (GSPC) method to identify influential nodes considering both the node attributes and the network topology. We first evaluate our GSPC method using two real-world datasets. The results show that our GSPC method effectively identifies influential nodes, which correspond well with the underlying ground truth. This is compatible to the previous eigenvector centrality and principal component centrality methods under circumstances where the nodes are homogeneous. In addition, spreading analysis shows that the GSPC method has a positive effect on the spreading dynamics.

Quantifying influential nodes in complex networks using optimization and particle dynamics: a comparative study

<title>Abstract</title> A soliton is a wave packet that maintains its particle-like and wave-like properties due to the balance betweendispersion and nonlinearity during propagation. By abstracting its main characteristics and allowing it totraverse a complex network according to certain rules, we investigated the relationship between the numberof solitons, the number of walk steps, and the frequency of node appearances in different networks. Usingthe Pearson coefficient, we demonstrated a strong correlation between increasing the number of solitonsand reducing the number of walk steps, as well as decreasing the number of solitons and increasing thenumber of walk steps. We also used the Jaccard coefficient to measure the overlap of important nodes acrossdifferent segments. Finally, we selected four real-world networks, Using an infection model, we obtained therelationship curves of infection rate versus time steps, under the condition that important nodes identifiedby various strategies are used as seed nodes. This provides a unique perspective for recognizing influentialnodes and demonstrates that the important nodes derived from soliton walks are effective in the propagationof information within dynamic infection models.

The identification of influential nodes in complex networks is one of the most exciting topics in network science. The latest work successfully compares each node using local connectivity and weak tie theory from a new perspective. We study the structural properties of networks in depth and extend this successful node evaluation from single-scale to multi-scale. In particular, one novel position parameter based on node transmission efficiency is proposed, which mainly depends on the shortest distances from target nodes to high-degree nodes. In this regard, the novel multi-scale information importance (MSII) method is proposed to better identify the crucial nodes by combining the network’s local connectivity and global position information. In simulation comparisons, five state-of-the-art algorithms, i.e. the neighbor nodes degree algorithm (NND), betweenness centrality, closeness centrality, Katz centrality and the k-shell decomposition method, are selected to compare with our MSII. The results demonstrate that our method obtains superior performance in terms of robustness and spreading propagation for both real-world and artificial networks.

Identifying influential nodes in complex networks by adjusted feature contributions and neighborhood impact