Importance Of Nodes In Network Research Articles

Similarity Analysis of Learning Interests among Majors Using Complex Networks

At present, multi-specialization cross integration is the new trend for high-level personnel training and scientific and technological innovation. A similarity analysis of learning interests among specializations based on book borrowing behavior is proposed in this paper. Students of different majors that borrow the same book can be regarded as a way of measuring similar learning interests among majors. Considering the borrowing data of 75 majors, 14,600 undergraduates, and 280,000 books at the Northwest Normal University (NWNU), as an example, this study classified readers into majors depending on similarity among students. A complex network of similar learning interests among specializations was constructed using group behavior data. The characteristics of learning interests were revealed among majors through a network topology analysis, importance of network nodes, and calculation of the similarity among different majors by the Louvain algorithm. The study concluded that the major co-occurrence network was characterized as scale-free and small-world; most majors had mutual communication and an infiltrating relationship, and the 75 majors of NWNU may form six major interest groups. The conclusions of the study were related to the development of majors of the university, and a match between major learning communities was based on the borrowing interest in a similar network to reflect the relationship between the characteristics and internal operating rules of a major.

GMM: A generalized mechanics model for identifying the importance of nodes in complex networks

How to assess the importance of nodes in the network is an open question. There are many ways to identify the importance of nodes in complex networks. However, these methods have their own shortcomings and advantages. In particular, some methods based on the importance of nodes between interactions between nodes have been proposed. These methods utilize local information or path information. How to combine local and global information is still a problem. In this paper, a generalized mechanical model is proposed that uses global information and local information. To verify the effectiveness of the method, some experiments were performed on a total of ten real networks. In particular, an innovative experimental network-based quality assessment was proposed to validate the method of identifying the importance of nodes.

Coreness and $h$ -Index for Weighted Networks

This paper presents a unified framework to generalize the traditional k-core decomposition method for both weighted and unweighted networks. It not only subsumes previous k-core decomposition methods but provides some new ones. With the help of the definition of n-th order h-index, we prove that all k-core indexes can be regarded as some steady state of h-index series with n going to infinity. Furthermore, all hindexes we obtain in intermediate calculation steps can be used as ranking scores to assess node importance in networks. Finally, we apply the provided new methods as well as two existing ones to four real networks and compare their performances on spreading influences ranking.

Efficient Updating of Node Importance in Dynamic Real-Life Networks

The analysis of real-life networks, such as the internet, biometrical networks, and social networks, is challenged by the constantly changing structure of these networks. Typically, such networks consist of multiple weakly connected subcomponents and efficiently updating the importance of network nodes, as captured by the ergodic projector of a random walk on these networks, is a challenging task. In this paper, new approximations are introduced that allow to efficiently update the ergodic projector of Markov multi-chains. Properties such as convergence and error bounds for approximations are established. The numerical applicability is illustrated with a real-life social network example.

Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory

Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS) tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers) collected in Tatra National Park (TNP), Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph). In a second step, the actual use of the area by skiers (functional network; directed graph) was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: β, γ, α), movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige) were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure.

An improved node algorithm based on the evaluation of weighted network node importance

There are shortcomings in the node contraction method used in the evaluation of the importance of weighted network nodes. To avoid those defects, an improved importance evaluation method is proposed. The differences of edge weight have impacts on importance of nodes and edges; therefore, two improvements are made in defining the network cohesion and the importance of edges of network G* using weighted shortest distances. In this paper, this improved method is analyzed and validated through a comparative analysis. The influence of the coefficients on the importance and relative importance of the nodes is analyzed by adjusting the proportional coefficient and the weight coefficient. The results show that the improved method can provide more comprehensive and accurate assessment of the importance of weighted network nodes without increasing the computational complexity.

Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory

AbstractComplex Network Theory can analyze the reliability of high-speed passenger traffic networks and also evaluate node importance. This paper conducts a systematic and in-depth research of importance of various nodes in the high-speed passenger traffic network so as to improve the high-speed passenger traffic network level. To study importance of network nodes can contribute to an in-depth understanding of the network structure. Therefore, the complex network is introduced and the node importance is evaluated. The characteristics of the complex network are briefly analyzed. In order to study the high-speed passenger traffic nodes, the network restraint coefficient, the network scale, the efficiency, the grade level, the partial clustering coefficient of degree and structural hole. Besides, the algorithm to calculate node importance is designed. Through analysis of the high-speed passenger network, the accuracy and practicability of the Complex Network Theory in evaluating node importance are pointed out. It is also proved that Complex Network Theory can help optimize high-speed passenger traffic networks and improve traffic efficiency.

A Node Importance Measuring Method based on Hypernetwork

Measuring the importance of nodes in network is an important issue in the study of complex networks. The networks in current researches are mostly based on classical graph theory, which have limitations on describing certain complex relations. In this work, we introduce hypernetwork, taking hypergraph as representation foundation, to describe relations. Hypernetwork is able to extend the modeling and describing capability of traditional network and may be a promising representation model of complex relations. However, a general lack of attention to the node importance measuring in hypernetwork, an important fundamental issue for its further application, has been noted across the majority of related published works. In this paper, we utilize the idea of deleting method, to measure the importance of node in hypernetwork through investigating the influence on the whole network when deleting it. Specifically, the influence is measured by direct loss and indirect loss. Through a calculating example, our method is compared with node degree, betweenness, closeness centrality, degree of neighbor nodes etc., the result shows this method has better adaptability and accuracy.

Internet Immunization Strategy based on Relations of Nodes

Inspired by the biological immune system against outside invasion in nature, this paper propose a network security strategy using Agent technology. The Agents with independent behavior capacity are set for resisting network intrusion using their spontaneous coordinate organization. Based on the comparisons of existing immunization strategies, such as target immune, acquaintance immune and random immunity, it is found that the importance of nodes in network are influenced by interaction between nodes, degree of nodes, information flow, and other factors. If the nodes are more important, they have a greater influence over the whole network. When important nodes are infected by virus, there will be a higher probability of spreading of hazard information. Therefore, this paper proposes a network security model using Agent technology, where important nodes are implanted with relationship immunization strategy. Experimental results show when the network suffered from random or malicious attacks, relationship immunization strategy is more effective than others existing methods.

Centrality Computation in Weighted Networks Based on Edge-Splitting Procedure

The analysis of network’s centralities has a high-level significance for many real-world applications. The variety of game and graph theoretical approaches has a paramount purpose to formalize a relative importance of nodes in networks. In this paper we represent an algorithm for the centrality calculation in the domain of weighted networks. The given algorithm calculates network centralities for weighted graphs based on the proposed procedure of edges’ splitting. The approach is tested and illustrated based on different types of network topologies.

Node Importance Measurement Based on the Degree and Closeness Centrality

In order to evaluate network node importance efiectively, an approach based on the node importance evaluation matrix is proposed. Difierent from previous node importance measurement approaches, the factors of the node degree and node closeness centrality comprehensively are considered. The time complexity of the algorithm is o(n 3 ). Finally, experimental results show the proposed approach is feasible and efiective.

Group centralization of network indices

In social network analysis various centrality indices are introduced to quantify importance of nodes in networks. Group centrality indices, introduced in 1999 by Borgatti and Everett, measure the importance of groups of nodes in networks. While centrality measures compare the importance of different nodes within a graph, the associated notion of centralization, as introduced in 1979 by Freeman allows us to compare the relative importance of nodes within their respective graphs. In this paper, we study the notion of group centralization with respect to eccentricity, degree and betweenness centrality measures. For groups of size 2, we determine the maximum achieved value of group eccentricity and group betweenness centralization and describe the corresponding extremal graphs. For group degree centralization we do the same with arbitrary size of group. We conclude with posing few open problems.

Recommendation of important nodes in deployment optimization model of defense strategy

Current network security defense strategy focuses on deploying to high degree nodes where there are mainly two aspects of the problem: One is that the high-degree nodes are not the backbone nodes for the network communication in many occasions; another is that these nodes are not always the most effective ones for forwarding and propagation information. With the disadvantage of current network defense strategy deployment, this paper tends to improve the traditional diffusion model of malicious program propagation and measure the importance of network nodes by using intermediate hops, then the important node for recommended deployment technology based on betweenness center control and closeness center control model is put forward. Experimental results show that the nodes with high betweenness centrality and low closeness centrality as compared with the high degree nodes can more effectively quarantine the spreading of the worms whether in scale-free network or in small world network. Meanwhile, the clustering behavior of a network will also play a certain negative impact on the spread of malicious programs.

Evaluating the structure and use of hiking trails in recreational areas using a mixed GPS tracking and graph theory approach

Recreational trails encourage numerous outdoor leisure activities in a variety of urban, rural, and natural environments. Understanding the way trails function is crucial for the designers and managers of recreational sites to balance the needs of visitors and site capacities. This paper presents a new approach to evaluate the structure and use of hiking trails by combining GPS tracking and analytical methods based on graph theory. The study is based upon empirical data (N = 482 GPS tracks) collected in the Lobau, which is part of the Danube Floodplains National Park in Austria. The physical structure of trails (structural network; undirected graph) and their usage (functional network; directed graph) were analysed using a graph theory approach. The network coherence (connectivity indices: β, γ, α), the movement direction at path segments and the relative importance of network nodes (node centrality measures: degree, closeness, betweenness) were calculated. The Lobau trail network is not evenly used by park visitors. Therefore, the calculated parameters differ between the structural and functional networks. From management perspective the results obtained for the functional network are particularly important. 61% of recreational use (hiking) concentrates on designated trails, 21% on non-marked paths and 18% is off-trail use. In most cases the location of signposts and information boards in the Lobau corresponds with the highest node centrality measures in the functional network (degree and betweenness). The proposed methodology can be easily adopted for the evaluation of any trail network in outdoor recreational sites.

The Solution to Node Importance in Complex Networks Based on PageRank Algorithm

Network science is an emerging interdiscipline that can solve practical issues by researching and analyzing properties of complex networks. In this paper, a modified algorithm based on PageRank is developed to construct the evaluation model in directed-weighted networks. This model can effectively determine the node importance in networks. Discussions about how to construct networks with the use of relationship between data and how to determine the weight of edges form the major concern of the present studies. Schemes for solving the above issues can differ in different networks. We successfully apply this model to citation, co-author and weibo follower networks. Through the results, we find that this optimized model can efficiently evaluate the importance of nodes in different complex networks and has strong applicability.

Robustness of network measures to link errors

In various applications involving complex networks, network measures are employed to assess the relative importance of network nodes. However, the robustness of such measures in the presence of link inaccuracies has not been well characterized. Here we present two simple stochastic models of false and missing links and study the effect of link errors on three commonly used node centrality measures: degree centrality, betweenness centrality, and dynamical importance. We perform numerical simulations to assess robustness of these three centrality measures. We also develop an analytical theory, which we compare with our simulations, obtaining very good agreement.

Study on Network Vulnerability Identification and Equilibrated Network Immunization Strategy

Network structure has a great impact both on hazard spread and network immunization. The vulnerability of the network node is associated with each other, assortative or disassortative. Firstly, an algorithm for vulnerability relevance clustering is proposed to show that the vulnerability community phenomenon is obviously existent in complex networks. On this basis, next, a new indicator called network “hyper-betweenness” is given for evaluating the vulnerability of network node. Network hyper-betweenness can reflect the importance of network node in hazard spread better. Finally, the dynamic stochastic process of hazard spread is simulated based on Monte-Carlo sampling method and a two-player, non-cooperative, constant-sum game model is designed to obtain an equilibrated network immunization strategy.

Identifying and characterizing nodes important to community structure using the spectrum of the graph.

BackgroundMany complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem.Methodology/Principal FindingsIn this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change in the eigenvalues of the network adjacency matrix upon their removal. Second, we also propose an index to distinguish two kinds of important nodes in communities, i.e., “community core” and “bridge”.Conclusions/SignificanceOur indices are only relied on the spectrum of the graph matrix. They are applied in many artificial networks as well as many real-world networks. This new methodology gives us a basic approach to solve this challenging problem and provides a realistic result.

Node Importance Assessment of Traffic Complex Network Based on C-Means Clustering

Hub nodes of urban traffic complex network are very important for region traffic signal control. Traditionally, region traffic signal control system like SCOOT/SCATS use traffic flow, vehicle queue and distance between junctions as reference in sub-control-area selection practice, in which process engineers’ experience should play importance roles. In this paper, node degree, node betweeness and high peak hour traffic flow are selected as indexes for traffic network node importance assessment. Moreover, C-Means clustering is applied to analysis which junction could be act as a hub node for regional traffic control. To test the effectiveness of this method, urban network around Chang’an Street in Beijing including almost fifty nodes, China is used as trail field. Data result shows Changchunjie, FuyoujieNankou and Hepingmen junction have high clustering characteristics when clustering number are 3, 4 and 5. And the clustering center shows very similar prosperities with real hub node in practice. In conclusion, the multi-index and clustering analysis could provide theoretical support for urban traffic complex network hub node assessment.

A new centrality measure based on sub-tree

How to evaluate the importance of nodes in networks and detect the centrality has become a vital problem in improving the efficiency of telecommunication and making a disease immunity strategy. We consider the mechanisms of real networks, and define a cost function to describe different hierarchies of networks to measure node importance. This method takes up a node’s regional influence as well as its global influence to evaluate its importance. The results of simulation prove that this method is proper to describe effectively and detect node discrepancies in a network.