Identifying influential nodes in complex networks: Effective distance gravity model

Excavating important nodes in complex networks based on the heat conduction model

Analyzing the important nodes of complex systems by complex network theory can effectively solve the scientific bottlenecks in various aspects of these systems, and how to excavate important nodes has become a hot topic in complex network research. This paper proposes an algorithm for excavating important nodes based on the heat conduction model (HCM), which measures the importance of nodes by their output capacity. The number and importance of a node's neighbors are first used to determine its own capacity, its output capacity is then calculated based on the HCM while considering the network density, distance between nodes, and degree density of other nodes. The importance of the node is finally measured by the magnitude of the output capacity. The similarity experiments of node importance, sorting and comparison experiments of important nodes, and capability experiments of multi-node infection are conducted in nine real networks using the Susceptible-Infected-Removed model as the evaluation criteria. Further, capability experiments of multi-node infection are conducted using the Independent cascade model. The effectiveness of the HCM is demonstrated through a comparison with eight other algorithms for excavating important nodes.

User Real-Time Influence Ranking Algorithm of Social Networks Considering Interactivity and Topicality

At present, the existing influence evaluation algorithms often ignore network structure attributes, user interests and the time-varying propagation characteristics of influence. To address these issues, this work comprehensively discusses users' own influence, weighted indicators, users' interaction influence and the similarity between user interests and topics, thus proposing a dynamic user influence ranking algorithm called UWUSRank. First, we determine the user's own basic influence based on their activity, authentication information and blog response. This improves the problem of poor objectivity of initial value on user influence evaluation when using PageRank to calculate user influence. Next, this paper mines users' interaction influence by introducing the propagation network properties of Weibo (a Twitter-like service in China) information and scientifically quantifies the contribution value of followers' influence to the users they follow according to different interaction influences, thereby solving the drawback of equal value transfer of followers' influence. Additionally, we analyze the relevance of users' personalized interest preferences and topic content and realize real-time monitoring of users' influence at various time periods during the process of public opinion dissemination. Finally, we conduct experiments by extracting real Weibo topic data to verify the effectiveness of introducing each attribute of users' own influence, interaction timeliness and interest similarity. Compared to TwitterRank, PageRank and FansRank, the results show that the UWUSRank algorithm improves the rationality of user ranking by 9.3%, 14.2%, and 16.7%, respectively, which proves the practicality of the UWUSRank algorithm. This approach can serve as a guide for research on user mining, information transmission methods, and public opinion tracking in social network-related areas.

Vital node identification in hypergraphs via gravity model

Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality problem has attracted much attention due to the challenge of how to utilize higher-order structure for the definition of centrality metrics. In this paper, we propose a new centrality method (HGC) on the basis of the gravity model as well as a semi-local HGC, which can achieve a balance between accuracy and computational complexity. Meanwhile, two comprehensive evaluation metrics, i.e., a complex contagion model in hypergraphs, which mimics the group influence during the spreading process and network s-efficiency based on the higher-order distance between nodes, are first proposed to evaluate the effectiveness of our methods. The results show that our methods can filter out nodes that have fast spreading ability and are vital in terms of hypergraph connectivity.

Exploring influential nodes using global and local information

In complex networks, key nodes are important factors that directly affect network structure and functions. Therefore, accurate mining and identification of key nodes are crucial to achieving better control and a higher utilization rate of complex networks. To address this problem, this paper proposes an accurate and efficient algorithm for critical node mining. The influential nodes are determined using both global and local information (GLI) to solve the shortcoming of the existing key node identification methods that consider either local or global information. The proposed method considers two main factors, global and local influences. The global influence is determined using the K-shell hierarchical information of a node, and local influence is obtained considering the number of edges connected by the node and the given values of adjacent nodes. The given values of adjacent nodes are determined based on the degree and K-shell hierarchical information. Further, the similarity coefficient of neighbors is considered, which enhances the differentiation degree of the adjacent given values. The proposed method solves the problems of the high complexity of global information-based algorithms and the low accuracy of local information-based algorithms. The proposed method is verified by simulation experiments using the SIR and SI models as a reference, and twelve typical real-world networks are used for the comparison. The proposed GLI algorithm is compared with several common algorithms at different periods. The comparison results show that the GLI algorithm can effectively explore influential nodes in complex networks.

Analysis of the Spatial Differentiation and Development Optimization of Towns’ Livable Quality in Aksu, China

With the proposal of the United Nations Sustainable Development Goals (SDGs), how to effectively improve the quality of human settlements has become a hot spot. Governments and scholars around the world pay attention to reasonable improvement of livability, which is conducive to improving the happiness level of residents and is closely related to human well-being. Due to the lack of rural statistical data in Xinjiang, this study established a new comprehensive evaluation system, which selected 21 indicators from the natural and humanistic aspects. The results show that the overall ecological security of Aksu prefecture is good, and Kuche city has the best humanistic livability performance. In terms of the livable quality of towns, Kuche Urban Area performs best. The towns with excellent and good livable quality are concentrated, but their spatial connections are weak. Based on the analysis and survey results, we put forward zoning optimization suggestions for the livable quality in Aksu prefecture. The results of this study would provide directional guidance for the improvement of livable quality in Aksu prefecture. At the same time, we expect that it can provide a methodological supplement for the relevant evaluation in other similar regions.

Identifying influential spreaders by gravity model considering multi-characteristics of nodes

How to identify influential spreaders in complex networks is a topic of general interest in the field of network science. Therefore, it wins an increasing attention and many influential spreaders identification methods have been proposed so far. A significant number of experiments indicate that depending on a single characteristic of nodes to reliably identify influential spreaders is inadequate. As a result, a series of methods integrating multi-characteristics of nodes have been proposed. In this paper, we propose a gravity model that effectively integrates multi-characteristics of nodes. The number of neighbors, the influence of neighbors, the location of nodes, and the path information between nodes are all taken into consideration in our model. Compared with well-known state-of-the-art methods, empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on ten real networks suggest that our model generally performs best. Furthermore, the empirical results suggest that even if our model only considers the second-order neighborhood of nodes, it still performs very competitively.

Gravity-Law Based Critical Bots Identification in Large-Scale Heterogeneous Bot Infection Network

The explosive growth of botnets has posed an unprecedented potent threat to the internet. It calls for more efficient ways to screen influential bots, and thus precisely bring the whole botnet down beforehand. In this paper, we propose a gravity-based critical bots identification scheme to assess the influence of bots in a large-scale botnet infection. Specifically, we first model the propagation of the botnet as a Heterogeneous Bot Infection Network (HBIN). An improved SEIR model is embedded into HBIN to extract both heterogeneous spatial and temporal dependencies. Within built-up HBIN, we elaborate a gravity-based influential bots identification algorithm where intrinsic influence and infection diffusion influence are specifically designed to disclose significant bots traits. Experimental results based on large-scale sample collections from the implemented prototype system demonstrate the promising performance of our scheme, comparing it with other state-of-the-art baselines.

Identifying influential spreaders in complex networks by an improved gravity model

Identification of influential spreaders is still a challenging issue in network science. Therefore, it attracts increasing attention from both computer science and physical societies, and many algorithms to identify influential spreaders have been proposed so far. Degree centrality, as the most widely used neighborhood-based centrality, was introduced into the network world to evaluate the spreading ability of nodes. However, degree centrality always assigns too many nodes with the same value, so it leads to the problem of resolution limitation in distinguishing the real influences of these nodes, which further affects the ranking efficiency of the algorithm. The k-shell decomposition method also faces the same problem. In order to solve the resolution limit problem, we propose a high-resolution index combining both degree centrality and the k-shell decomposition method. Furthermore, based on the proposed index and the well-known gravity law, we propose an improved gravity model to measure the importance of nodes in propagation dynamics. Experiments on ten real networks show that our model outperforms most of the state-of-the-art methods. It has a better performance in terms of ranking performance as measured by the Kendall's rank correlation, and in terms of ranking efficiency as measured by the monotonicity value.