Influential Nodes Identification in Complex Networks via Information Entropy

Finding influential nodes in complex networks based on Kullback-Leibler model within the neighborhood

As a research hot topic in the field of network security, the implementation of machine learning, such as federated learning, involves information interactions among a large number of distributed network devices. If we regard these distributed network devices and connection relationships as a complex network, we can identify the influential nodes to find the crucial points for optimizing the imbalance of the reliability of devices in federated learning system. This paper will analyze the advantages and disadvantages of existing algorithms for identifying influential nodes in complex networks, and propose a method from the perspective of information dissemination for finding influential nodes based on Kullback-Leibler divergence model within the neighborhood (KLN). Firstly, the KLN algorithm removes a node to simulate the scenario of node failure in the information dissemination process. Secondly, KLN evaluates the loss of information entropy within the neighborhood after node removal by establishing the KL divergence model. Finally, it assesses the damage influence of the removed node by integrating the network attributes and KL divergence model, thus achieving the evaluation of node importance. To validate the performance of KLN, this paper conducts an analysis and comparison of its results with those of 11 other algorithms on 10 networks, using SIR model as a reference. Additionally, a case study was undertaken on a real epidemic propagation network, leading to the proposal of management and control strategies for daily protection based on the influential nodes. The experimental results indicate that KLN effectively evaluates the importance of the removed node using KL model within the neighborhood, and demonstrate better accuracy and applicability across networks of different scales.

Exploring the Entropy Complex Networks with Latent Interaction

In the present work, we study the introduction of a latent interaction index, examining its impact on the formation and development of complex networks. This index takes into account both observed and unobserved heterogeneity per node in order to overcome the limitations of traditional compositional similarity indices, particularly when dealing with large networks comprising numerous nodes. In this way, it effectively captures specific information about participating nodes while mitigating estimation problems based on network structures. Furthermore, we develop a Shannon-type entropy function to characterize the density of networks and establish optimal bounds for this estimation by leveraging the network topology. Additionally, we demonstrate some asymptotic properties of pointwise estimation using this function. Through this approach, we analyze the compositional structural dynamics, providing valuable insights into the complex interactions within the network. Our proposed method offers a promising tool for studying and understanding the intricate relationships within complex networks and their implications under parameter specification. We perform simulations and comparisons with the formation of Erdös-Rényi and Barabási-Alber-type networks and Erdös-Rényi and Shannon-type entropy. Finally, we apply our models to the detection of microbial communities.

Identifying Influential Nodes in Social Networks: Exploiting Self-Voting Mechanism

The influence maximization (IM) problem is defined as identifying a group of influential nodes in a network such that these nodes can affect as many nodes as possible. Due to its great significance in viral marketing, disease control, social recommendation, and so on, considerable efforts have been devoted to the development of methods to solve the IM problem. In the literature, VoteRank and its improved algorithms have been proposed to select influential nodes based on voting approaches. However, in the voting process of these algorithms, a node cannot vote for itself. We argue that this voting schema runs counter to many real scenarios. To address this issue, we designed the VoteRank* algorithm, in which we first introduce the self-voting mechanism into the voting process. In addition, we also take into consideration the diversities of nodes. More explicitly, we measure the voting ability of nodes and the amount of a node voting for its neighbors based on the H-index of nodes. The effectiveness of the proposed algorithm is experimentally verified on 12 benchmark networks. The results demonstrate that VoteRank* is superior to the baseline methods in most cases.

The Structure Entropy-Based Node Importance Ranking Method for Graph Data

Due to its wide application across many disciplines, how to make an efficient ranking for nodes in graph data has become an urgent topic. It is well-known that most classical methods only consider the local structure information of nodes, but ignore the global structure information of graph data. In order to further explore the influence of structure information on node importance, this paper designs a structure entropy-based node importance ranking method. Firstly, the target node and its associated edges are removed from the initial graph data. Next, the structure entropy of graph data can be constructed by considering the local and global structure information at the same time, in which case all nodes can be ranked. The effectiveness of the proposed method was tested by comparing it with five benchmark methods. The experimental results show that the structure entropy-based node importance ranking method performs well on eight real-world datasets.

Detecting influential nodes with topological structure via Graph Neural Network approach in social networks

Detecting influential nodes in complex social networks is crucial due to the enormous amount of data and the constantly changing behavior of existing topologies. Centrality-based and machine-learning approaches focus mostly on node topologies or feature values in their evaluation of nodes' relevance. However, both network topologies and node attributes should be taken into account when determining the influential value of nodes. This research has proposed a deep learning model called Graph Convolutional Networks (GCN) to discover the significant nodes in graph-based large datasets. A deep learning framework for identifying influential nodes with structural centrality via Graph Convolutional Networks called DeepInfNode has been developed. The proposed approach measures up contextual information from Susceptible-Infected-Recovered (SIR) model trials to measure the rate of infection to develop node representations. In the experimental section, acquired experimental results indicate that the suggested model has a higher F1 and Area under the curve (AUC) value. The findings indicate that the strategy is both effective and precise in terms of suggesting new linkages. The proposed DeepInfNode model outperforms state-of-the-art approaches on a variety of publicly available standard graph datasets, achieving an increase in performance of up to 99.1% of accuracy.

The Self-Information Weighting-Based Node Importance Ranking Method for Graph Data

Due to their wide application in many disciplines, how to make an efficient ranking for nodes, especially for nodes in graph data, has aroused lots of attention. To overcome the shortcoming that most traditional ranking methods only consider the mutual influence between nodes but ignore the influence of edges, this paper proposes a self-information weighting-based method to rank all nodes in graph data. In the first place, the graph data are weighted by regarding the self-information of edges in terms of node degree. On this base, the information entropy of nodes is constructed to measure the importance of each node and in which case all nodes can be ranked. To verify the effectiveness of this proposed ranking method, we compare it with six existing methods on nine real-world datasets. The experimental results show that our method performs well on all of these nine datasets, especially for datasets with more nodes.

The structure and information spread capability of the network formed by integrated fitness apps

Purpose

In this article we aim to understand how the network formed by fitness tracking devices and associated apps as a subset of the broader health-related Internet of things is capable of spreading information.

Design/methodology/approach

The authors used a combination of a content analysis, network analysis, community detection and simulation. A sample of 922 health-related apps (including manufacturers' apps and developers) were collected through snowball sampling after an initial content analysis from a Google search for fitness tracking devices.

Findings

The network of fitness apps is disassortative with high-degree nodes connecting to low-degree nodes, follow a power-law degree distribution and present with low community structure. Information spreads faster through the network than an artificial small-world network and fastest when nodes with high degree centrality are the seeds.

Practical implications

This capability to spread information holds implications for both intended and unintended data sharing.

Originality/value

The analysis confirms and supports evidence of widespread mobility of data between fitness and health apps that were initially reported in earlier work and in addition provides evidence for the dynamic diffusion capability of the network based on its structure. The structure of the network enables the duality of the purpose of data sharing.

An ICN-Based IPFS High-Availability Architecture

The Interplanetary File System (IPFS), a new type of P2P file system, enables people to obtain data from other peer nodes in a distributed system without the need to establish a connection with a distant server. However, IPFS suffers from low resolution efficiency and duplicate data delivery, resulting in poor system availability. The new Information-Centric Networking (ICN), on the other hand, applies the features of name resolution service and caching to achieve fast location and delivery of content. Therefore, there is a potential to optimize the availability of IPFS systems from the network layer. In this paper, we propose an ICN-based IPFS high-availability architecture, called IBIHA, which introduces enhanced nodes and information tables to manage data delivery based on the original IPFS network, and uses the algorithm of selecting high-impact nodes from the entitled network (PwRank) as the basis for deploying enhanced nodes in the network, thus achieving the effect of optimizing IPFS availability. The experimental results show that this architecture outperforms the IPFS network in terms of improving node resolution efficiency, reducing network redundant packets, and improving the rational utilization of network link resources.

Adjacency-Information-Entropy-Based Cooperative Name Resolution Approach in ICN

Information-centric networking (ICN) is an emerging network architecture that has the potential to address low-transmission latency and high-reliability requirements in the fifth generation and beyond communication networks (5G/B5G). In the ICN architectures that use the identifier–locator separation mode, a name resolution system (NRS) is an important infrastructure for managing and maintaining the mappings between identifiers and locators. To meet the demands of time-sensitive applications, researchers have developed a distributed local NRS that can provide name resolution service within deterministic latency, which means it can respond to a name resolution request within a latency upper bound. However, processing name resolution requests only locally cannot take full advantage of the potential of the distributed local NRS. In this paper, we propose a name resolution approach, called adjacency-information-entropy-based cooperative name resolution (ACNR). In ACNR, when a name resolution node receives a name resolution request from a user, it can use neighboring name resolution nodes to respond to this request in a parallel processing manner. For this purpose, ACNR uses the information entropy that takes into account the adjacency and latency between name resolution nodes to describe the local structure of nodes efficiently. The proposed approach is extensively validated on simulated networks. Compared with several other approaches, the experiment results show that ACNR can discover more cooperative neighbors in a reasonable communication overhead, and achieve a higher name resolution success rate.

Identifying Influential Nodes in Complex Networks Based on Multiple Local Attributes and Information Entropy

Identifying influential nodes in complex networks has attracted the attention of many researchers in recent years. However, due to the high time complexity, methods based on global attributes have become unsuitable for large-scale complex networks. In addition, compared with methods considering only a single attribute, considering multiple attributes can enhance the performance of the method used. Therefore, this paper proposes a new multiple local attributes-weighted centrality (LWC) based on information entropy, combining degree and clustering coefficient; both one-step and two-step neighborhood information are considered for evaluating the influence of nodes and identifying influential nodes in complex networks. Firstly, the influence of a node in a complex network is divided into direct influence and indirect influence. The degree and clustering coefficient are selected as direct influence measures. Secondly, based on the two direct influence measures, we define two indirect influence measures: two-hop degree and two-hop clustering coefficient. Then, the information entropy is used to weight the above four influence measures, and the LWC of each node is obtained by calculating the weighted sum of these measures. Finally, all the nodes are ranked based on the value of the LWC, and the influential nodes can be identified. The proposed LWC method is applied to identify influential nodes in four real-world networks and is compared with five well-known methods. The experimental results demonstrate the good performance of the proposed method on discrimination capability and accuracy.

Identifying Important Nodes in Complex Networks Based on Node Propagation Entropy

In recent years, the identification of the essential nodes in complex networks has attracted significant attention because of their theoretical and practical significance in many applications, such as preventing and controlling epidemic diseases and discovering essential proteins. Several importance measures have been proposed from diverse perspectives to identify crucial nodes more accurately. In this paper, we propose a novel importance metric called node propagation entropy, which uses a combination of the clustering coefficients of nodes and the influence of the first- and second-order neighbor numbers on node importance to identify essential nodes from an entropy perspective while considering the local and global information of the network. Furthermore, the susceptible–infected–removed and susceptible–infected–removed–susceptible epidemic models along with the Kendall coefficient are used to reveal the relevant correlations among the various importance measures. The results of experiments conducted on several real networks from different domains show that the proposed metric is more accurate and stable in identifying significant nodes than many existing techniques, including degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and H-index.

Influential nodes identification using network local structural properties

With the rapid development of information technology, the scale of complex networks is increasing, which makes the spread of diseases and rumors harder to control. Identifying the influential nodes effectively and accurately is critical to predict and control the network system pertinently. Some existing influential nodes detection algorithms do not consider the impact of edges, resulting in the algorithm effect deviating from the expected. Some consider the global structure of the network, resulting in high computational complexity. To solve the above problems, based on the information entropy theory, we propose an influential nodes evaluation algorithm based on the entropy and the weight distribution of the edges connecting it to calculate the difference of edge weights and the influence of edge weights on neighbor nodes. We select eight real-world networks to verify the effectiveness and accuracy of the algorithm. We verify the infection size of each node and top-10 nodes according to the ranking results by the SIR model. Otherwise, the Kendall \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ coefficient is used to examine the consistency of our algorithm with the SIR model. Based on the above experiments, the performance of the LENC algorithm is verified.

COVID-19 Symptoms app analysis to foresee healthcare impacts: Evidence from Northern Ireland

Mobile health (mHealth) technologies, such as symptom tracking apps, are crucial for coping with the global pandemic crisis by providing near real-time, in situ information for the medical and governmental response. However, in such a dynamic and diverse environment, methods are still needed to support public health decision-making. This paper uses the lens of strong structuration theory to investigate networks of COVID-19 symptoms in the Belfast metropolitan area. A self-supervised machine learning method measuring information entropy was applied to the Northern Ireland COVIDCare app. The findings reveal: (1) relevant stratifications of disease symptoms, (2) particularities in health-wealth networks, and (3) the predictive potential of artificial intelligence to extract entangled knowledge from data in COVID-related apps. The proposed method proved to be effective for near real-time in-situ analysis of COVID-19 progression and to focus and complement public health decisions. Our contribution is relevant to an understanding of SARS-COV-2 symptom entanglements in localised environments. It can assist decision-makers in designing both reactive and proactive health measures that should be personalised to the heterogeneous needs of different populations. Moreover, near real-time assessment of pandemic symptoms using digital technologies will be critical to create early warning systems of emerging SARS-CoV-2 strains and predict the need for healthcare resources.

Role-Aware Information Spread in Online Social Networks

Understanding the complex process of information spread in online social networks (OSNs) enables the efficient maximization/minimization of the spread of useful/harmful information. Users assume various roles based on their behaviors while engaging with information in these OSNs. Recent reviews on information spread in OSNs have focused on algorithms and challenges for modeling the local node-to-node cascading paths of viral information. However, they neglected to analyze non-viral information with low reach size that can also spread globally beyond OSN edges (links) via non-neighbors through, for example, pushed information via content recommendation algorithms. Previous reviews have also not fully considered user roles in the spread of information. To address these gaps, we: (i) provide a comprehensive survey of the latest studies on role-aware information spread in OSNs, also addressing the different temporal spreading patterns of viral and non-viral information; (ii) survey modeling approaches that consider structural, non-structural, and hybrid features, and provide a taxonomy of these approaches; (iii) review software platforms for the analysis and visualization of role-aware information spread in OSNs; and (iv) describe how information spread models enable useful applications in OSNs such as detecting influential users. We conclude by highlighting future research directions for studying information spread in OSNs, accounting for dynamic user roles.

Identifying critical higher-order interactions in complex networks

Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Identification of nodes influence based on global structure model in complex networks

Identification of Influential nodes in complex networks is challenging due to the largely scaled data and network sizes, and frequently changing behaviors of the current topologies. Various application scenarios like disease transmission and immunization, software virus infection and disinfection, increased product exposure and rumor suppression, etc., are applicable domains in the corresponding networks where identification of influential nodes is crucial. Though a lot of approaches are proposed to address the challenges, most of the relevant research concentrates only on single and limited aspects of the problem. Therefore, we propose Global Structure Model (GSM) for influential nodes identification that considers self-influence as well as emphasizes on global influence of the node in the network. We applied GSM and utilized Susceptible Infected Recovered model to evaluate its efficiency. Moreover, various standard algorithms such as Betweenness Centrality, Profit Leader, H-Index, Closeness Centrality, Hyperlink Induced Topic Search, Improved K-shell Hybrid, Density Centrality, Extended Cluster Coefficient Ranking Measure, and Gravity Index Centrality are employed as baseline benchmarks to evaluate the performance of GSM. Similarly, we used seven real-world and two synthetic multi-typed complex networks along-with different well-known datasets for experiments. Results analysis indicates that GSM outperformed the baseline algorithms in identification of influential node(s).

Identifying influential nodes: A new method based on network efficiency of edge weight updating

Identification of influential nodes in complex networks is an area of exciting growth since it can help us to deal with various problems. Furthermore, identifying important nodes can be used across various disciplines, such as disease, sociology, biology, engineering, just to name a few. Hence, how to identify influential nodes more accurately deserves further research. Traditional identification methods usually only focus on the local or global information of the network. However, only focusing on a part of the information in the network will lead to the loss of information, resulting in inaccurate results. In order to address this problem, an identification method based on network efficiency of edge weight updating is proposed, which can effectively incorporate both global and local information of the network. Our proposed method avoids the lack of information in the network and ensures the accuracy of the results as much as possible. Moreover, by introducing the iterative idea of weight updating, some dynamic information is also introduced into our proposed method, which is more convincing. Varieties of experiments have been carried out on 11 real-world data sets to demonstrate the effectiveness and superiority of our proposed method.

A Survey of Information Entropy Metrics for Complex Networks

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.