PageRank Values Research Articles

ON THE INITIAL VALUE OF PAGERANK

Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also applied to undirected networks. In this paper, we have applied PageRank to undirected networks, showing that a vertex’s PageRank relies on its initial value, often referred to as an intrinsic, non-network contribution. We have analytically proved that when the initial value of vertices is either proportional to their degrees or set to zero, the PageRank values of the vertices become directly proportional to their degrees. Simulated and empirical data are employed to bolster our research findings. Additionally, we have investigated the impact of initial values on PageRank localization.

Construction of Metaphorical Maps of Cyberspace Resources Based on Point‐Cluster Feature Generalization

ABSTRACTIn the digital age, the expansion of cyberspace has resulted in increasing complexity, making clear cyberspace visualization crucial for effective analysis and decision‐making. Current cyberspace visualizations are overly complex and fail to accurately reflect node importance. To address the challenge of complex cyberspace visualization, this study introduces the integrated centrality metric (ICM) for constructing a metaphorical map that accurately reflects node importance. The ICM, a novel node centrality measure, demonstrates superior accuracy in identifying key nodes compared to degree centrality (DC), k‐shell centrality (KC), and PageRank values. Through community partitioning and point‐cluster feature generalization, we extract a network's hierarchical structure to intuitively represent its community and backbone topology, and we construct a metaphorical map that offers a clear visualization of cyberspace. Experiments were conducted on four original networks and their extracted backbone networks to identify core nodes. The Jaccard coefficient was calculated considering the results of the three aforementioned centrality measures, ICM, and the SIR model. The results indicate that ICM achieved the best performance in both the original networks and all extracted backbone networks. This demonstrates that ICM can more precisely evaluate node importance, thereby facilitating the construction of metaphorical maps. Moreover, the proposed metaphorical map is more convenient than traditional topological maps for quickly comprehending the complex characteristics of networks.

Efficient and Accurate PageRank Approximation on Large Graphs

PageRank is a commonly used measurement in a wide range of applications, including search engines, recommendation systems, and social networks. However, this measurement suffers from huge computational overhead, which cannot be scaled to large graphs. Although many approximate algorithms have been proposed for computing PageRank values, these algorithms are either (i) not efficient or (ii) not accurate. Worse still, some of them cannot provide estimated PageRank values for all the vertices. In this paper, we first propose the CUR-Trans algorithm, which can reduce the time complexity for computing PageRank values and has lower error bound than existing matrix approximation-based PageRank algorithms. Then, we develop the T 2 -Approx algorithm to further reduce the time complexity for computing this measurement. Experiment results on three large-scale graphs show that both the CUR-Trans algorithm and the T 2 -Approx algorithm achieve the lowest response time for computing PageRank values with the best accuracy (for the CUR-Trans algorithm) or the competitive accuracy (for the T 2 -Approx algorithm). Besides, the two proposed algorithms are able to provide estimated PageRank values for all the vertices.

Predicting Scientific Breakthroughs Based on Structural Dynamic of Citation Cascades

Predicting breakthrough papers holds great significance; however, prior studies encountered challenges in this task, indicating a need for substantial improvement. We propose that the failure to capture the dynamic structural-evolutionary features of citation networks is one of the major reasons. To overcome this limitation, this paper introduces a new method for constructing citation cascades of focus papers, allowing the creation of a time-series-like set of citation cascades. Then, through a thorough review, three types of structural indicators in these citation networks that could reflect breakthroughs are identified, including certain basic topological metrics, PageRank values, and the von Neumann graph entropy. Based on the time-series-like set of citation cascades, the dynamic trajectories of these indicators are calculated and employed as predictors. Using the Nobel Prize-winning papers as a landmark dataset, our prediction method yields approximately a 7% improvement in the ROC-AUC score compared to static-based prior methods. Additionally, our method advances in achieving earlier predictions than other previous methods. The main contribution of this paper is proposing a novel method for creating citation cascades in chronological order and confirming the significance of predicting breakthroughs from a dynamic structural perspective.

Risk Evolution Analysis of Seafarers’ Unsafe Acts in Maritime Accidents Based on Directed Weighted CN

Seafarers’ unsafe acts as the direct causes of maritime accidents are considered to be the result of the interaction between complex and dynamic influencing factors. Identifying the risk evolution characteristics and paths of seafarers’ unsafe acts has always been a challenge in maritime safety management. For this purpose, the present study introduces association rule technique into complex network to develop a directed weighted interaction network of seafarers’ unsafe acts and their influencing factors. Through global network topology analysis and local network community detection, the risk evolution characteristics of seafarers’ unsafe acts in maritime accidents are analyzed from a multidimensional perspective. The results indicate that the developed network has small-world characteristics, and the top 10 critical nodes all belong to seafarers’ unsafe acts, of which failure to make proper sound and light signals achieves the highest PageRank value. Results from this study would help maritime stakeholders to understand the evolution mechanism of seafarers’ unsafe acts and develop safety management strategies for interrupting the risk propagation of seafarers’ unsafe acts.

Statistical analysis of the regional air quality index of Yangtze River Delta based on complex network theory

Air pollution is an urgent global issue with significant implications for the environment and public health. This study focuses on the daily Air Quality Index (AQI) data from 27 major cities in the Yangtze River Delta (YRD) region of China spanning 2017-2022. Firstly, we establish an optimal threshold for constructing a stable AQI-weighted directed network, considering time lag coefficients and correlation coefficients. Quarterly analyses of correlation coefficients and time lag distribution among cities are conducted. Secondly, we apply complex network theory to examine the basic properties of the AQI-weighted directed network. Thirdly, integrating traditional methods and PageRank values, we identify crucial nodes, emphasizing key cities like Nantong, Nanjing, and Yangzhou in air quality management. Finally, utilizing the Louvain algorithm, three community structure divisions led by influential city nodes are dynamically identified. This study offers a valuable framework for collaborative air pollution management in the Yangtze River Delta, promoting improved air quality and sustainable urban development.

On the development and measurement of human factors complex network for maritime accidents: A case of ship groundings

Human factors from organizational aspects to unsafe behaviors of the crew on board form a directed complex network reflecting the evolution of maritime accidents. The present study aims to develop a human factors complex network contributing to maritime accidents. First, a maritime accident scenario is defined based on 104 ship grounding accident reports, then the human factors contributing to ship groundings are identified and structured within HFACS using grounding theory. Second, chi-square tests and odd ratio analysis are employed to capture the interrelationships among these human factors within HFACS, which are then represented as nodes, edges, and edge weights in network. The topological parameters including degree, clustering coefficients, and node importance are measured in the end for the human factors complex network. The results indicate that the factor “Inadequate safety management by the shipping company” belonged to Organizational influences has the highest influence on the factors “Not taken safe ship speeds”, “Improper lashing and stowage”, “Failure to implement the planned route”, and “Failure to keep navigational AIDS in normally open operation’ that belonged to Unsafe acts, while these unsafe acts have the highest PageRank value, affirming their direct role in causing maritime accidents. Results from this study are valuable for understanding of the network propagation mechanism of human factor risks in maritime accidents, and can also offer guidance to shipping companies, maritime authorities, and relevant stakeholders in establishing and optimizing human factor barriers in such accidents.

Synthesizing social insurance research: A bibliometric analysis

Social insurance has been a pivotal tool in implementing social security. The purpose of the study is to analyze the existing information clusters (areas) in the field of social insurance. Clusters define related and unrelated groups in the field of social insurance. These groups will help streamline and identify areas where little or no research has been conducted to present. To achieve the objective, the study employed a precise and systematic procedure to gather 562 journal articles published in Scopus-indexed journals from 1926–2022. Subsequently, VOSviewer, Science of Science (Sci2), and Gephi were utilized to conduct bibliometric analysis (such as keyword co-occurrence and bibliographic coupling) and network analysis tests (such as citation and co-citation analysis). The results of keyword co-occurrence and co-citation analysis suggest there are three knowledge clusters: welfare provisions, benefits provided by social insurance, and social insurance operational aspects. Through analysis found top article-based Inequality, social insurance, and redistribution with 408(LC) and 1042(GC) and its page rank value is 0.010574 through prestigious analysis. Additionally, it is also observed that I. Nielsen had made the most substantial contributions as an author, with R. Smyth and C. Nyland following closely in the rankings. Also, observed maximum total link strength with 109 value on social security variable. The study also drawn attention to specific deficiencies, including regional concentration of research, insufficient research in developing and underdeveloped countries, inadequate knowledge sharing among researchers, limited methodological diversity, and a lack of research on the role of social insurance in facilitating society’s recovery from the pandemic.

Understanding dockless bike-sharing spatiotemporal travel patterns: Evidence from ten cities in China

Dockless bike-sharing (DBS) has gained popularity in many cities in recent years. However, little attention has been given to the commonalities and differences in DBS travel patterns from multiple cities. This study aims to fill this gap by comparing DBS travel patterns in ten Chinese cities of varying scales. It collected data from these cities and analysed them from two perspectives: service usage characteristics and complex network properties. The results reveal a coexistence of similarities and differences in DBS travel patterns across different cities. The ten major cities show significant similarities in temporal distribution, with a similarity coefficient exceeding 0.7. Southern cities have a higher percentage of night riding compared to their northern counterparts. Moreover, over 85% of the travel distances are within 2 km. Concerning spatial distribution, all ten cities demonstrate an imbalanced demand distribution during peak hours, particularly in downtown areas, exhibiting evident tidal patterns. Network analysis outcomes demonstrate that the DBS networks in all ten cities possess small-world and scale-free properties. Furthermore, nodes with high degree centrality and closeness centrality are predominantly concentrated in downtown areas, displaying a diminishing trend from the city centre to the outskirts and showcasing strong global spatial autocorrelation. The betweenness centrality exhibits a property of random distribution. Nodes with high PageRank values are mainly concentrated in the city centre and around metro stations. The findings offer valuable insights for transportation planners and managers seeking to enhance their understanding of DBS systems.

Drug Repositioning Based on a Multiplex Network by Integrating Disease, Gene, and Drug Information

Background: The research of new drugs is very expensive and the cycle is relatively long, so it has broad development prospects and good economic benefits to use validated drugs in the treatment of other diseases. Objective: The purpose of drug repositioning is to identify other indications for existing drugs. In addition to using disease and drug information for drug repositioning, other biomolecular information can also be integrated for drug repositioning. Integrating multiple biomolecular data of different types can improve the predictive performance of drug repositioning models. Methods: This paper proposes a drug repositioning algorithm based on a multiplex network (DRMN algorithm) by integrating disease, gene, and drug information. DRMN algorithm utilizes known disease-gene and gene-drug associations to connect disease phenotype similarity network, gene expression similarity network, and drug response similarity network. Then they are constructed into a multiplex network, and the importance score of each node is calculated by PageRank (PR) algorithm. Finally, disease-drug association scores are sorted to achieve drug repositioning. Results: DRMN algorithm is applied to two sets of sample data. Disease-drug association scores are calculated separately from disease PR values and drug PR values in both datasets. In top 50% of association scores, lots of disease-drug association prediction results have been verified by existing results. Compared with other algorithms, DRMN algorithm also shows better performance. Conclusion: DRMN algorithm can effectively integrate multi-omics data for drug repositioning and obtain better prediction results.

Risk evolution and prevention and control strategies of maritime accidents in China's coastal areas based on complex network models

The increasingly busy maritime traffic system has resulted in frequent maritime accidents. To prevent maritime accidents, we investigated and studied typical cases of maritime accidents along the coast of China in recent years. Based on the complex network theory, a network model of China's coastal maritime traffic accidents is constructed from the four risk factors of human-ship-environmental-management. On this basis, the overall structural characteristics of the maritime accident network are analyzed according to the characteristic parameters of the complex network. In addition, based on the node betweenness and PageRank value, the network robustness analysis is carried out, the key factors in the maritime accidents are excavated and risk prevention and control measures are proposed. The research shows that the average path length of the marine traffic accident network is short, the clustering coefficient is high, and the risk spreads quickly in the network and passes through fewer nodes, which can lead to the occurrence of accidents. Through the management and control of key risk factors, the evolution of risks can be effectively blocked and the large and above maritime accidents can be reduced.

Analysis of Students Performance in Mathematics before and during Covid-19 Pandemic using PageRank: A Preliminary Study

In a normal situation, a university is constantly utilizing standard statistical analysis tools to provide a student's ranking through their academic achievement. The tools provides analysis of pairwise comparison among students on their academic performance but unfortunately visualization of the results is limited to the use of line graph, histogram, tables and boxplot which are not easily explained. In this study, another way of analyzing the pairwise comparison of academic performance on Mathematics among students is introduced that is by using interaction graph which is based on a weighted directed graph approach. The ranking of student’s performance in Mathematics is calculated using Page Rank (PR) algorithm. A sample of final examination result for twenty-one students whom enrolled in Mathematics courses in Fakulti Sains Komputer dan Matematik (FSKM), UiTM Shah Alam are investigated. Their performance by marks in two Mathematics courses taken before the pandemic and three Mathematics courses taken during the pandemic are analyzed. The graph with twenty-one nodes represent the students, while the directed links between two students represent the Mathematics relative performance is established. The rank of the students’ Mathematics performance is obtained from PR value of the graph. The largest PR value indicates the highest performance of the respective student. The result revealed that 62 percent of the students have shown better Mathematics performance even though the learning platforms before and during Covid-19 pandemic were drastically changed. Although this result does not indicate the whole picture of FSKM students' Mathematics performance, it gives a good insight to the academic administrator in making better decision. Besides, the interaction graph provides an easy way to explain the result only by looking into the graph.

Google pagerank algorithm: using efficient damping factor

A vital feature of modern web search engine is the ability to display relevant and reputable pages near the top of the list of query results. A well-used search engine nowadays is Google search engine, it is the world's most popular search engine, rely on PageRank technology to determine a website's ranking. We put our attention on important benefactions to improving the quality of rankings via the value which is called damping factor, commonly the original suggestion d=0.85 by Brin and Page is the most common choice. In this paper, we suggest a new value which plays an important role to rank web sites accurately, our work focuses on damping factor value which improves the efficiency of PageRank value for each website. Our results show that the suggested value can get greater performance. Finally, we will show satisfactory result without link spam and dangling node applying PageRank algorithm on graphs with over 5000 links.

The product marketing model of the economic zone by the sensor big data mining algorithm

Since the reform and opening up, China's market economy has gradually prospered, and the development of various industries and their products has become a key research issue of the government. In the context of big data, this article believes that future industrial development should be driven by big data. At the same time, the advent of the era of big data will surely bring about changes in the marketing model of products in the economic zone. This article puts forward the research on product marketing model based on big data mining algorithm, the purpose is to do a detailed investigation of the core algorithm of data mining, in order to improve the marketing efficiency of enterprises and reduce the investment and loss of marketing. The method of this paper is to study the Hadoop parallel framework and the K-Means algorithm in the mining algorithm to collaboratively filter the big data mining algorithm, and integrate these algorithms into the marketing process. These methods can recommend products to target users based on their previous interests and other users who have similar interests. Finally, this article sorts the web pages according to the PageRank value of each node in order to achieve the purpose of accurately recommending products to customers. Through the K-means algorithm mining data experiment and financial product marketing examples, this article puts forward some suggestions and measures for the marketing model. The experimental results show that the customer response rate of precision marketing is 11.92 % higher than that of ordinary marketing, and the sales efficiency of marketers has improved significantly. In addition, precision marketing is better than ordinary marketing in many aspects such as the proportion of large orders, average consumption price, and refund rate.

A Normalized Rich-Club Connectivity-Based Strategy for Keyword Selection in Social Media Analysis

In this paper, we present a study on keyword selection behavior in social media analysis that is focused on particular topics, and propose a new effective strategy that considers the co-occurrence relationships between keywords and uses graph-based techniques. In particular, we used the normalized rich-club connectivity considering the weighted degree, closeness centrality, betweenness centrality and PageRank values to measure a subgroup of highly connected “rich keywords” in a keyword co-occurrence network. Community detection is subsequently applied to identify several keyword combinations that are able to accurately and comprehensively represent the researched topic. The empirical results based on four topics and comparing four existing models confirm the performance of our proposed strategy in promoting the quantity and ensuing the quality of data related to particular topics collected from social media. Overall, our findings are expected to offer useful guidelines on how to select keywords for social media-based studies and thus further increase the reliability and validity of their respective conclusions.

Influence of an interurban innovation network on the innovation capacity of China: A multiplex network perspective

Interurban innovation network is a typical multiplex network formed by the interactive coupling of spaces of flows of technology cooperation and transfer. However, studies investigating interurban innovation network from a multiplex network are rare. This study constructs an interurban technology cooperation-transfer network based on the multiplex network perspective and uses spatial Durbin model to reveal the mechanism of its structural characteristics on the urban innovation capability. It finds that: (1) There is a large variability in China's urban innovation capability, which are mainly reflected in the differences between cities in the eastern region and other regions. The China's urban innovation capability presents obvious spatial heterogeneity and agglomeration characteristics. (2) China's interurban technology cooperation-transfer network possesses high spatial coupling. The degree-strength division boundary of the network is clear-cut. Additionally, the degree-strength division and Pagerank classification show a certain level of spatial coincidence and correlation characteristics, with the community space being agglomerated. (3) In the relationship between China's interurban technology cooperation-transfer network structure embeddedness and urban innovation capability, the node degree and urban innovation capability possesses a U-shaped relationship. The node strength and Pagerank value have positive effects on urban innovation capability. Meanwhile, the node Pagerank value has significant positive spatial spillover effect, while node degree and strength both have significant negative spatial spillover effects. These findings can be used to develop a more effective interurban innovation network that will help the innovative development of Chinese cities.

An Urban Hot/Cold Spot Detection Method Based on the Page Rank Value of Spatial Interaction Networks Constructed from Human Communication Records

Applying spatial clustering algorithms on large-scale spatial interactive dataset to find urban hot/cold spots is a new idea to assist urban management. However, the research usually focuses on the dataset with spatio-temporal proximity, rather than remote dataset. This article proposes a spatial hot/cold spot detection method for human communication by auto-correlating the PageRank values of the spatial interaction networks constructed by records. Milan was selected as the study area, and the spatial interaction records reflected by telephone calls, the land-use dataset, and the POI dataset were used as experimental data. The results showed that the proposed method can be applied to long-distance spatial interactive recording data, and the hot/cold spot were clearly distinguished by the statistical distribution of the containing land-use dataset and the POI dataset. These differences were consistent with the actual situation in the study area, indicating the accuracy of the proposed method for detecting hot/cold areas.

Roadmap to hydrogen society of Tokyo: Locating priority of hydrogen facilities based on multiple big data fusion

Hydrogen socialization has become a promising target in future energy development. Hydrogen fuel cell vehicle is gradually becoming a considerable substitute for fossil fuel vehicles in many countries. As for the promotion of hydrogen fuel cell vehicles, The construction of facilities like hydrogen refueling stations and depots should be strengthened. The research provides a case study of locating the priority of the construction of hydrogenation facilities, based on policy regulation, massive GPS trajectory records, geographical land use data, road network and, POI data. The PageRank value in the complex network theory is employed to estimate the priority of the Land use Unit and policies regulation is referred to to ensure the feasibility of construction. Among 24,595 Land Use Units in sum, 59.78% of them are allowed to build hydrogen facilities. The results show that the available location of hydrogen refueling stations with high priority (we pick the first 100 for analysis) and feasibility in policy are geographically clustered around the city centers and sub-centers. The place with the highest PageRank value of 0.0033 is Haneda airport, which is an important transportation hub. The PageRank values of most of the other first 100 ranked Land Use Units are under 0.001. This indicates that the vehicle transportation network is highly centralized. There is an obvious sequence of priority of hydrogen refueling stations. We furtherly provide sensitivity analysis and it shows that higher-ranked places are spatially clustered. The best hydrogen depot is located near Tokyo Bay with the advantage of low transportation cost of liquid hydrogen, convenient transportation conditions, strong safety assurance. After verification, the results showed consistency with the current hydrogenation facility construction process and demonstrated the potential for future hydrogenation facility construction.

Detection and evolution analysis of TCM patent community based on weighted complex network

In order to provide help and support for the analysis, mining, research, and development of traditional Chinese medicines, and for the discovery of medicine evolution laws, a weighted complex network based medicine community detection algorithm is proposed. Firstly, a weighted network of herbs is constructed according to the correlation degrees between nodes; and then, nodes with the highest PageRank (PR) value are selected iteratively as the initial clustering centres of the community; lastly, the nodes with the highest similarity to the nodes in the community are added to the community one by one, until all the nodes are divided into the corresponding TCM community. We verify the stability and effectiveness of the algorithm on the classic test networks. The algorithm is applied to the community detection and evolution analysis of antihypertensive TCM patents to obtain the core herbs and their evolution laws.

Identification of critical nodes for cascade faults of grids based on electrical PageRank

In this paper, the electrical PageRank method is proposed to identify the critical nodes in a power grid considering cascading faults as well as directional weighting. This method can rapidly and accurately focus on the critical nodes in the power system. First, the proposed method simulates the scenario in a grid after a node is attacked by cascading faults. The load loss of the grid is calculated. Second, the electrical PageRank algorithm is proposed. The nodal importance of a grid is determined by considering cascading faults as well as directional weights. The electrical PageRank values of the system nodes are obtained based on the proposed electrical PageRank algorithm and ranked to identify the critical nodes in a grid. Finally, the effectiveness of the proposed method is verified using the IEEE39 node system. The proposed method is highly effective in preventing the occurrence of cascading faults in power systems.