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.

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.

Use of Centrality Metrics for Ranking of Courses Based on Their Relative Contribution in a Curriculum Network Graph

2018 ◽  
pp. 129-159
Keyword(s):  
Betweenness Centrality ◽  
Directed Acyclic Graph ◽  
Degree Centrality ◽  
Weighted Sum ◽  
Eigenvector Centrality ◽  
Network Graph ◽  
Curriculum Assessment ◽  
Acyclic Graph ◽  
Relative Contribution ◽  
Centrality Metrics

The author proposes a centrality and topological sort-based formulation to quantify the relative contribution of courses in a curriculum network graph (CNG), a directed acyclic graph, comprising of the courses (as vertices), and their pre-requisites (captured as directed edges). The centrality metrics considered are out-degree and in-degree centrality along with betweenness centrality and eigenvector centrality. The author normalizes the values obtained for each centrality metric as well as the level numbers of the vertices in a topological sort of the CNG. The contribution score for a vertex is the weighted sum of the normalized values for the vertex. The author observes the betweenness centrality of the vertices (courses) to have the largest influence in the relative contribution scores of the courses that could be used as a measure of the weights to be given to the courses for curriculum assessment and student ranking as well as to cluster courses with similar contribution.

Centrality Metrics-Based Connected Dominating Sets for Real-World Network Graphs

2019 ◽  
pp. 1-29
Author(s):  
Natarajan Meghanathan ◽  
Md Atiqur Rahman ◽  
Mahzabin Akhter
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Degree Centrality ◽  
Dominating Sets ◽  
Eigenvector Centrality ◽  
Connected Dominating Sets ◽  
The Real ◽  
Centrality Metrics ◽  
Local Clustering Coefficient ◽  
Node Size

The authors investigate the use of centrality metrics as node weights to determine connected dominating sets (CDS) for a suite of 60 real-world network graphs of diverse degree distribution. They employ centrality metrics that are neighborhood-based (degree centrality [DEG] and eigenvector centrality [EVC]), shortest path-based (betweenness centrality [BWC] and closeness centrality [CLC]) as well as the local clustering coefficient complement-based degree centrality metric (LCC'DC), which is a hybrid of the neighborhood and shortest path-based categories. The authors target for minimum CDS node size (number of nodes constituting the CDS). Though both the BWC and CLC are shortest path-based centrality metrics, they observe the BWC-based CDSs to be of the smallest node size for about 60% of the real-world networks and the CLC-based CDSs to be of the largest node size for more than 40% of the real-world networks. The authors observe the computationally light LCC'DC-based CDS node size to be the same as the computationally heavy BWC-based CDS node size for about 50% of the real-world networks.

Centrality-Based Assortativity Analysis of Complex Network Graphs

2018 ◽  
pp. 66-77
Keyword(s):  
Complex Network ◽  
Real World ◽  
Betweenness Centrality ◽  
Closeness Centrality ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Centrality Metrics

In this chapter, the author analyzes the assortativity of real-world networks based on centrality metrics (such as eigenvector centrality, betweenness centrality, and closeness centrality) other than degree centrality. They seek to evaluate the levels of assortativity (assortative, dissortative, neutral) observed for real-world networks with respect to the different centrality metrics and assess the similarity in these levels. The author observes real-world networks are more likely to be neutral (neither assortative nor dissortative) with respect to both R-DEG and BWC, and more likely to be assortative with respect to EVC and CLC. They observe the chances of a real-world network to be dissortative with respect to these centrality metrics to be very minimal. The author also assesses the extent to which they can use the assortativity index (A.Index) values obtained with a computationally light centrality metric to rank the networks in lieu of the A.Index values obtained with a computationally heavy centrality metric.

Centrality and Partial Correlation Coefficient-Based Assortativity Analysis of Real-World Networks

2018 ◽  
Vol 62 (9) ◽  
pp. 1247-1264 ◽  
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Correlation Coefficient ◽  
Real World ◽  
Betweenness Centrality ◽  
Partial Correlation ◽  
Closeness Centrality ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
First Order ◽  
Centrality Metrics ◽  
Partial Correlation Coefficient

Abstract The assortativity index (A. Index) of a complex network has been hitherto computed as the Pearson’s correlation coefficient of the remaining degree centrality (R-DEG) of the first-order neighbors (i.e. end vertices of the edges) in the network. In this paper, we seek to evaluate the assortativity of real-world networks with respect to prototypical centrality metrics (in addition to R-DEG) such as eigenvector centrality (EVC), betweenness centrality (BWC) and closeness centrality (CLC). Unlike R-DEG, the centrality values of the vertices with respect to these three metrics are influenced by the centrality values of the vertices in the neighborhood. We propose to use the notion of ‘Partial Correlation Coefficient’ to nullify the influence of the second-order neighbors (i.e. vertices that are two hops away) and quantify the assortativity of the first-order neighbors with respect to a particular centrality metric (such as EVC, BWC and CLC). We conduct an exhaustive assortativity analysis on a suite of 70 real-world networks of diverse degree distributions. We observe real-world networks to be more assortative (A. Index > 0) with respect to CLC and EVC and relatively more dissortative (A. Index < 0) with respect to BWC and R-DEG.

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2019 ◽  
pp. 1183-1198
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

The authors present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. They consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC), and betweenness centrality (BWC). They define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. The authors observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. They observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2018 ◽  
pp. 6507-6521
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

We present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. We consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC) and betweenness centrality (BWC). We define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. We observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. We observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

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.

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.

A NEW CENTRALITY METRIC BASED ON CLUSTERING COEFFICIENT

2013 ◽  
Vol 24 (07) ◽  
pp. 1350043
Author(s):  
CHONG LI ◽  
SHI-ZE GUO ◽  
ZHE-MING LU ◽  
YU-LONG QIAO ◽  
GUANG-HUA SONG
Keyword(s):  
Network Analysis ◽  
Information Transmission ◽  
Complex Network ◽  
Betweenness Centrality ◽  
Flow Simulation ◽  
Clustering Coefficient ◽  
Simulation Experiments ◽  
Centrality Metrics ◽  
Entire Network ◽  
Simulated Flow

Many centrality metrics have been proposed over the years to compute the centrality of nodes, which has been a key issue in complex network analysis. The most important node can be estimated through a variety of metrics, such as degree, closeness, eigenvector, betweenness, flow betweenness, cumulated nominations and subgraph. Simulated flow is a common method adopted by many centrality metrics, such as flow betweenness centrality, which assumes that the information spreads freely in the entire network. Generally speaking, the farther the information travels, the more times the information passes the geometric center. Thus, it is easy to determine which node is more likely to be the center of the geometry network. However, during information transmission, different nodes do not share the same vitality, and some nodes are more active than others. Therefore, the product of one node's degree and its clustering coefficient can be viewed as a good factor to show how active this node is. In this paper, a new centrality metric called vitality centrality is introduced, which is only based on this product and the simulated flow. Simulation experiments based on six test networks have been carried out to demonstrate the effectiveness of our new metric.

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