Node Importance Ranking of Complex Networks with Entropy Variation

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.

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.

Integrated Bayesian and association-rules methods for autonomously orienting COVID-19 patients

The coronavirus infection continues to spread rapidly worldwide, having a devastating impact on the health of the global population. To fight against COVID-19, we propose a novel autonomous decision-making process which combines two modules in order to support the decision-maker: (1) Bayesian Networks method-based data-analysis module, which is used to specify the severity of coronavirus symptoms and classify cases as mild, moderate, and severe, and (2) autonomous decision-making module-based association rules mining method. This method allows the autonomous generation of the adequate decision based on the FP-growth algorithm and the distance between objects. To build the Bayesian Network model, we propose a novel data-based method that enables to effectively learn the network's structure, namely, MIGT-SL algorithm. The experimentations are performed over pre-processed discrete dataset. The proposed algorithm allows to correctly generate 74%, 87.5%, and 100% of the original structure of ALARM, ASIA, and CANCER networks. The proposed Bayesian model performs well in terms of accuracy with 96.15% and 94.77%, respectively, for binary and multi-class classification. The developed decision-making model is evaluated according to its utility in solving the decisional problem, and its accuracy of proposing the adequate decision is about 97.80%.

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.

Node Importance Identification for Temporal Networks Based on Optimized Supra-Adjacency Matrix

The research on node importance identification for temporal networks has attracted much attention. In this work, combined with the multi-layer coupled network analysis method, an optimized supra-adjacency matrix (OSAM) modeling method was proposed. In the process of constructing an optimized super adjacency matrix, the intra-layer relationship matrixes were improved by introducing the edge weight. The inter-layer relationship matrixes were formed by improved similarly and the inter-layer relationship is directional by using the characteristics of directed graphs. The model established by the OSAM method accurately expresses the structure of the temporal network and considers the influence of intra- and inter-layer relationships on the importance of nodes. In addition, an index was calculated by the average of the sum of the eigenvector centrality indices for a node in each layer and the node importance sorted list was obtained from this index to express the global importance of nodes in temporal networks. The experimental results on three real temporal network datasets Enron, Emaildept3, and Workspace showed that compared with the SAM and the SSAM methods, the OSAM method has a faster message propagation rate and larger message coverage and better SIR and NDCG@10 indicators.

Causality-Network-Based Critical Hazard Identification for Railway Accident Prevention: Complex Network-Based Model Development and Comparison

This study investigates a critical hazard identification method for railway accident prevention. A new accident causation network is proposed to model the interaction between hazards and accidents. To realize consistency between the most likely and shortest causation paths in terms of hazards to accidents, a method for measuring the length between adjacent nodes is proposed, and the most-likely causation path problem is first transformed to the shortest causation path problem. To identify critical hazard factors that should be alleviated for accident prevention, a novel critical hazard identification model is proposed based on a controllability analysis of hazards. Five critical hazard identification methods are proposed to select critical hazard nodes in an accident causality network. A comparison of results shows that the combination of an integer programming-based critical hazard identification method and the proposed weighted direction accident causality network considering length has the best performance in terms of accident prevention.

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.

Influential Nodes Identification in Complex Networks via Information Entropy

Identifying a set of influential nodes is an important topic in complex networks which plays a crucial role in many applications, such as market advertising, rumor controlling, and predicting valuable scientific publications. In regard to this, researchers have developed algorithms from simple degree methods to all kinds of sophisticated approaches. However, a more robust and practical algorithm is required for the task. In this paper, we propose the EnRenew algorithm aimed to identify a set of influential nodes via information entropy. Firstly, the information entropy of each node is calculated as initial spreading ability. Then, select the node with the largest information entropy and renovate its l-length reachable nodes’ spreading ability by an attenuation factor, repeat this process until specific number of influential nodes are selected. Compared with the best state-of-the-art benchmark methods, the performance of proposed algorithm improved by 21.1%, 7.0%, 30.0%, 5.0%, 2.5%, and 9.0% in final affected scale on CEnew, Email, Hamster, Router, Condmat, and Amazon network, respectively, under the Susceptible-Infected-Recovered (SIR) simulation model. The proposed algorithm measures the importance of nodes based on information entropy and selects a group of important nodes through dynamic update strategy. The impressive results on the SIR simulation model shed light on new method of node mining in complex networks for information spreading and epidemic prevention.

Key Node Ranking in Complex Networks: A Novel Entropy and Mutual Information-Based Approach

Numerous problems in many fields can be solved effectively through the approach of modeling by complex network analysis. Finding key nodes is one of the most important and challenging problems in network analysis. In previous studies, methods have been proposed to identify key nodes. However, they rely mainly on a limited field of local information, lack large-scale access to global information, and are also usually NP-hard. In this paper, a novel entropy and mutual information-based centrality approach (EMI) is proposed, which attempts to capture a far wider range and a greater abundance of information for assessing how vital a node is. We have developed countermeasures to assess the influence of nodes: EMI is no longer confined to neighbor nodes, and both topological and digital network characteristics are taken into account. We employ mutual information to fix a flaw that exists in many methods. Experiments on real-world connected networks demonstrate the outstanding performance of the proposed approach in both correctness and efficiency as compared with previous approaches.

Identifying Node Importance in a Complex Network Based on Node Bridging Feature

Identifying node importance in complex networks is of great significance to improve the network damage resistance and robustness. In the era of big data, the size of the network is huge and the network structure tends to change dynamically over time. Due to the high complexity, the algorithm based on the global information of the network is not suitable for the analysis of large-scale networks. Taking into account the bridging feature of nodes in the local network, this paper proposes a simple and efficient ranking algorithm to identify node importance in complex networks. In the algorithm, if there are more numbers of node pairs whose shortest paths pass through the target node and there are less numbers of shortest paths in its neighborhood, the bridging function of the node between its neighborhood nodes is more obvious, and its ranking score is also higher. The algorithm takes only local information of the target nodes, thereby greatly improving the efficiency of the algorithm. Experiments performed on real and synthetic networks show that the proposed algorithm is more effective than benchmark algorithms on the evaluation criteria of the maximum connectivity coefficient and the decline rate of network efficiency, no matter in the static or dynamic attack manner. Especially in the initial stage of attack, the advantage is more obvious, which makes the proposed algorithm applicable in the background of limited network attack cost.

Node-Based Resilience Measure Clustering with Applications to Noisy and Overlapping Communities in Complex Networks

This paper examines a schema for graph-theoretic clustering using node-based resilience measures. Node-based resilience measures optimize an objective based on a critical set of nodes whose removal causes some severity of disconnection in the network. Beyond presenting a general framework for the usage of node based resilience measures for variations of clustering problems, we experimentally validate the usefulness of such methods in accomplishing the following: (i) clustering a graph in one step without knowing the number of clusters a priori; (ii) removing noise from noisy data; and (iii) detecting overlapping communities. We demonstrate that this clustering schema can be applied successfully using a wide range of data, including both real and synthetic networks, both natively in graph form and also expressed as point sets.

Calculation of the Connected Dominating Set Considering Vertex Importance Metrics

The computation of a set constituted by few vertices to define a virtual backbone supporting information interchange is a problem that arises in many areas when analysing networks of different natures, like wireless, brain, or social networks. Recent papers propose obtaining such a set of vertices by computing the connected dominating set (CDS) of a graph. In recent works, the CDS has been obtained by considering that all vertices exhibit similar characteristics. However, that assumption is not valid for complex networks in which their vertices can play different roles. Therefore, we propose finding the CDS by taking into account several metrics which measure the importance of each network vertex e.g., error probability, entropy, or entropy variation (EV).