Measures and metrics

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Network Structure ◽  
Similarity Measures ◽  
Clustering Coefficient ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Structural Balance ◽  
Important Nodes

This chapter describes the measures and metrics that are used to quantify network structure. The chapter starts with a discussion of centrality measures, which are used to identify central or important nodes in networks. Measures discussed include degree centrality, eigenvector centrality, PageRank, closeness, and betweenness. This is followed by a discussion of groupings of nodes like cliques and components, transitivity measures including the clustering coefficient, structural balance in networks, similarity measures, and assortative mixing.

scholarly journals A COMPARISON OF CENTRALITY MEASURES IN SUSTAINABLE DEVELOPMENT GOALS

2020 ◽  
Vol 14 (3) ◽  
pp. 309-320
Author(s):  
Sena Ariesandy ◽  
Ema Carnia ◽  
Herlina Napitupulu
Keyword(s):  
Sustainable Development ◽  
Millennium Development Goals ◽  
Sustainable Development Goals ◽  
Closeness Centrality ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Global Problems ◽  
Calculation Results ◽  
Development Goals

The Millennium Development Goals (MDGs), which began in 2000 with 8 goal points, have not been able to solve the global problems. The MDGs were developed into Sustainable Development Goals (SDGs) in 2015 with 17 targeted goal points achieved in 2030. Until now, methods for determining the priority of SDGs are still attractive to researchers. Centrality is one of the tools in determining the priority goal points on a network by using graph theory. There are four measurements of centrality used in this paper, namely degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. The calculation results obtained from the four measurements are compared, analyzed, to conclud which goal points are the most prior and the least prior. From the results obtained the most priority goal points in Sustainable Development Goals.

Computationally Light vs. Computationally Heavy Centrality Metrics

2018 ◽  
pp. 34-65
Keyword(s):  
Betweenness Centrality ◽  
Clustering Coefficient ◽  
Degree Centrality ◽  
Strongly Correlated ◽  
Eigenvector Centrality ◽  
Correlation Measure ◽  
Centrality Metrics ◽  
Two Measures ◽  
Local Clustering Coefficient ◽  
Spearman’S Correlation

In this chapter, the authors analyze the correlation between the computationally light degree centrality (DEG) and local clustering coefficient complement-based degree centrality (LCC'DC) metrics vs. the computationally heavy betweenness centrality (BWC), eigenvector centrality (EVC), and closeness centrality (CLC) metrics. Likewise, they also analyze the correlation between the computationally light complement of neighborhood overlap (NOVER') and the computationally heavy edge betweenness centrality (EBWC) metric. The authors analyze the correlations at three different levels: pair-wise (Kendall's correlation measure), network-wide (Spearman's correlation measure), and linear regression-based prediction (Pearson's correlation measure). With regards to the node centrality metrics, they observe LCC'DC-BWC to be the most strongly correlated at all the three levels of correlation. For the edge centrality metrics, the authors observe EBWC-NOVER' to be strongly correlated with respect to the Spearman's correlation measure, but not with respect to the other two measures.

Temporal Variation of the Node Centrality Metrics for Scale-Free Networks

2018 ◽  
pp. 78-97
Keyword(s):  
Temporal Variation ◽  
Closeness Centrality ◽  
The Other ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Scale Free Networks ◽  
Free Network

Scale-free networks are a type of complex networks in which the degree distribution of the nodes is according to the power law. In this chapter, the author uses the widely studied Barabasi-Albert (BA) model to simulate the evolution of scale-free networks and study the temporal variation of degree centrality, eigenvector centrality, closeness centrality, and betweenness centrality of the nodes during the evolution of a scale-free network according to the BA model. The model works by adding new nodes to the network, one at a time, with the new node connected to m of the currently existing nodes. Accordingly, nodes that have been in the network for a longer time have greater chances of acquiring more links and hence a larger degree centrality. While the degree centrality of the nodes has been observed to show a concave down pattern of increase with time, the temporal (time) variation of the other centrality measures has not been analyzed until now.

scholarly journals Node and Edge Eigenvector Centrality for Hypergraphs

2021 ◽  
Author(s):  
Francesco Tudisco ◽  
Desmond Higham
Keyword(s):  
Eigenvalue Problems ◽  
Point Of View ◽  
Centrality Measures ◽  
Data Sets ◽  
Power Method ◽  
Eigenvector Centrality ◽  
Nonlinear Eigenvalue Problems ◽  
Pairwise Interactions ◽  
Important Nodes ◽  
Realistic Data

Abstract Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting directly for higher order interactions, notably through a hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define and analyze a class of spectral centrality measures for identifying important nodes and hyperedges in hypergraphs, generalizing existing network science concepts. By exploiting the latest developments in nonlinear Perron-Frobenius theory, we show how the resulting constrained nonlinear eigenvalue problems have unique solutions that can be computed efficiently via a nonlinear power method iteration. We illustrate the measures on realistic data sets.

Centrality Metrics, Measures, and Real-World Network Graphs

2018 ◽  
pp. 1-33
Keyword(s):  
Real World ◽  
Betweenness Centrality ◽  
Closeness Centrality ◽  
Clustering Coefficient ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Centrality Metrics ◽  
Edge Betweenness ◽  
Correlation Measures ◽  
Local Clustering Coefficient

This chapter provides an introduction to various node and edge centrality metrics that are studied throughout this book. The authors describe the procedure to compute these metrics and illustrate the same with an example. The node centrality metrics described are degree centrality (DEG), eigenvector centrality (EVC), betweenness centrality (BWC), closeness centrality (CLC), and the local clustering coefficient complement-based degree centrality (LCC'DC). The edge centrality metrics described are edge betweenness centrality (EBWC) and neighborhood overlap (NOVER). The authors then describe the three different correlation measures—Pearson's, Spearman's, and Kendall's measures—that are used in this book to analyze the correlation between any two centrality metrics. Finally, the authors provide a brief description of the 50 real-world network graphs that are studied in some of the chapters of this book.

scholarly journals A Survey on Recent Methods of Finding Influential Nodes in Complex Networks

2021 ◽  
Vol 10 (2) ◽  
pp. 816-823
Keyword(s):  
Complex Networks ◽  
Time Complexity ◽  
Closeness Centrality ◽  
Clustering Coefficient ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Computation Complexity ◽  
Influential Nodes ◽  
New Challenges ◽  
Virus Spreading

Influential nodes refer to the ability of a node to spread information in complex networks. Identifying influential nodes is an important problem in complex networks which plays a key role in many applications such as rumor controlling, virus spreading, viral market advertising, research paper views, and citations. Basic measures like degree centrality, betweenness centrality, closeness centrality are identifying influential nodes but they are incapable of largescale networks due to time complexity issues. Chen et al. [1] proposed semi-local centrality, which is reducing computation complexity and finding influential nodes in the network. Recently Yang et al. 2020 [2] proposed a novel centrality measure based on degree and clustering coefficient for identifying the influential nodes. Sanjay et al. 2020 [3] gave voterank and neighborhood coreness-based algorithms for finding the influenced nodes in the network. Zhiwei et al. 2019 [4] considered the average shortest path to discover the influenced node in the network. These are the few recent local,global and mixed centralities. In this paper, we show a broad view of recent methods for finding influential nodes in complex networks. It also analyzes the new challenges and limitations for a better understanding of each method in detail. The experimental results based on these methods show better performance compared with existing basic centrality measures.

scholarly journals Node and edge nonlinear eigenvector centrality for hypergraphs

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Francesco Tudisco ◽  
Desmond J. Higham
Keyword(s):  
Eigenvalue Problems ◽  
Point Of View ◽  
Centrality Measures ◽  
Data Sets ◽  
Power Method ◽  
Eigenvector Centrality ◽  
Nonlinear Eigenvalue Problems ◽  
Pairwise Interactions ◽  
Important Nodes ◽  
Realistic Data

AbstractNetwork scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting directly for higher order interactions, notably through a hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define and analyze a class of spectral centrality measures for identifying important nodes and hyperedges in hypergraphs, generalizing existing network science concepts. By exploiting the latest developments in nonlinear Perron−Frobenius theory, we show how the resulting constrained nonlinear eigenvalue problems have unique solutions that can be computed efficiently via a nonlinear power method iteration. We illustrate the measures on realistic data sets.

scholarly journals Modeling the Public Transport Networks: A Study of Their Efficiency

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Mary Luz Mouronte-López
Keyword(s):  
Public Transportation ◽  
Probability Distributions ◽  
Transportation Network ◽  
Characteristic Curve ◽  
Similarity Measures ◽  
Centrality Measures ◽  
Cumulative Probability ◽  
Eigenvector Centrality ◽  
The Public ◽  
The Impact

The public transportation network (PTN) provides mobility and access to community resources, employment, medical care, infrastructures, and other resources in the city. This research studies the process of the formation of links among nodes in different real-world PTNs. We have found that this process may be appropriately explained by a generalized linear model (GLM) using local, global, and quasilocal similarity indexes as explanatory variables. In modeling, the response variable was described by a binomial probability density function, and the logit function was used as a link function. In the crossvalidation process, utilising a downsampling approach, both average accuracy and area under the receiver operating characteristic curve (AUC) metrics presented higher values than 0.99. The kappa parameter had magnitudes larger than 0.93 for most of the PTNs. In the final validation stage, recall and specificity metrics took the value 1. Accuracy and precision parameters were larger than 0.99 and 0.87, respectively, for the majority of PTNs. Only one of the PTNs required utilising a smoothed bootstrap approach in order to achieve better results. The similarity measures with the greatest influence on the model were determined. We also assessed the impact of link removal on the global efficiency of PTNs, considering several similarity indexes. Additionally, we find that most of the networks show low local and global efficiencies (≤0.20), as well as travel times with a relevant variability, exhibiting standard deviations larger than 790 seconds. Significant similarities exist between the cumulative probability distributions of the local efficiency in all PTNs. With respect to the centrality measures, the eigenvector centrality presented a strong correlation with the hub/authority centralities (>0.80), while the pagerank showed a moderate, high, or very high correlation with the degree in all PTNs, >0.50.

Centrality Measures

2018 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
State Of The Art ◽  
Centrality Measures ◽  
Eigenvector Centrality ◽  
Multilayer Networks ◽  
Comprehensive Description ◽  
Multilayer Network ◽  
Suitable Definition ◽  
Katz Centrality ◽  
Pagerank Centrality

Defining the centrality of nodes and layers in multilayer networks is of fundamental importance for a variety of applications from sociology to biology and finance. This chapter presents the state-of-the-art centrality measures able to characterize the centrality of nodes, the influences of layers or the centrality of replica nodes in multilayer and multiplex networks. These centrality measures include modifications of the eigenvector centrality, Katz centrality, PageRank centrality and Communicability to the multilayer network scenario. The chapter provides a comprehensive description of the research of the field and discusses the main advantages and limitations of the different definitions, allowing the readers that wish to apply these techniques to choose the most suitable definition for his or her case study.

scholarly journals Visualization of clinical teaching citations using social network analysis

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Hakimeh Hazrati ◽  
Shoaleh Bigdeli ◽  
Seyed Kamran Soltani Arabshahi ◽  
Vahideh Zarea Gavgani ◽  
Nafiseh Vahed
Keyword(s):  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Research Collaboration ◽  
Clinical Teaching ◽  
Clustering Coefficient ◽  
Knowledge Network ◽  
Research Network ◽  
Centrality Measures ◽  
The Usa

Abstract Background Analyzing the previous research literature in the field of clinical teaching has potential to show the trend and future direction of this field. This study aimed to visualize the co-authorship networks and scientific map of research outputs of clinical teaching and medical education by Social Network Analysis (SNA). Methods We Identified 1229 publications on clinical teaching through a systematic search strategy in the Scopus (Elsevier), Web of Science (Clarivate Analytics) and Medline (NCBI/NLM) through PubMed from the year 1980 to 2018.The Ravar PreMap, Netdraw, UCINet and VOSviewer software were used for data visualization and analysis. Results Based on the findings of study the network of clinical teaching was weak in term of cohesion and the density in the co-authorship networks of authors (clustering coefficient (CC): 0.749, density: 0.0238) and collaboration of countries (CC: 0.655, density: 0.176). In regard to centrality measures; the most influential authors in the co-authorship network was Rosenbaum ME, from the USA (0.048). More, the USA, the UK, Canada, Australia and the Netherlands have central role in collaboration countries network and has the vertex co-authorship with other that participated in publishing articles in clinical teaching. Analysis of background and affiliation of authors showed that co-authorship between clinical researchers in medicine filed is weak. Nineteen subject clusters were identified in the clinical teaching research network, seven of which were related to the expected competencies of clinical teaching and three related to clinical teaching skills. Conclusions In order to improve the cohesion of the authorship network of clinical teaching, it is essential to improve research collaboration and co-authorship between new researchers and those who have better closeness or geodisk path with others, especially those with the clinical background. To reach to a dense and powerful topology in the knowledge network of this field encouraging policies to be made for international and national collaboration between clinicians and clinical teaching specialists. In addition, humanitarian and clinical reasoning need to be considered in clinical teaching as of new direction in the field from thematic aspects.

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