Benchmark for Discriminating Power of Edge Centrality Metrics

2021 ◽  
Author(s):  
Qi Bao ◽  
Wanyue Xu ◽  
Zhongzhi Zhang
Keyword(s):  
Real World ◽  
Centrality Measures ◽  
Crucial Issue ◽  
Discriminating Power ◽  
Fast Approach ◽  
Centrality Metrics ◽  
Model Networks

Abstract Edge centrality has found wide applications in various aspects. Many edge centrality metrics have been proposed, but the crucial issue that how good the discriminating power of a metric is, with respect to other measures, is still open. In this paper, we address the question about the benchmark of the discriminating power of edge centrality metrics. We first use the automorphism concept to define equivalent edges, based on which we introduce a benchmark for the discriminating power of edge centrality measures and develop a fast approach to compare the discriminating power of different measures. According to the benchmark, for a desirable measure, equivalent edges have identical metric scores, while inequivalent edges possess different scores. However, we show that even in a toy graph, inequivalent edges cannot be discriminated by three existing edge centrality metrics. We then present a novel edge centrality metric called forest centrality (FC). Extensive experiments on real-world networks and model networks indicate that FC has better discriminating power than three existing edge centrality metrics.

Comparison and Application of Metrics That Define the Components Modularity in Complex Products

2008 ◽  
Author(s):  
Qi D. Van Eikema Hommes
Keyword(s):  
Social Network ◽  
Centrality Measures ◽  
Software Systems ◽  
Network Centrality ◽  
Good Pair ◽  
Centrality Metrics ◽  
The Social ◽  
Social Network Centrality ◽  
Sample Test

As the content and variety of technology increases in automobiles, the complexity of the system increases as well. Decomposing systems into modules is one of the ways to manage and reduce system complexity. This paper surveys and compares a number of state-of-art components modularity metrics, using 8 sample test systems. The metrics include Whitney Index (WI), Change Cost (CC), Singular value Modularity Index (SMI), Visibility-Dependency (VD) plot, and social network centrality measures (degree, distance, bridging). The investigation reveals that WI and CC form a good pair of metrics that can be used to assess component modularity of a system. The social network centrality metrics are useful in identifying areas of architecture improvements for a system. These metrics were further applied to two actual vehicle embedded software systems. The first system is going through an architecture transformation. The metrics from the old system revealed the need for the improvements. The second system was recently architected, and the metrics values showed the quality of the architecture as well as areas for further improvements.

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).

scholarly journals Spatio-temporal networks: reachability, centrality and robustness

2016 ◽  
Vol 3 (6) ◽  
pp. 160196 ◽  
Author(s):  
Matthew J. Williams ◽  
Mirco Musolesi
Keyword(s):  
Real World ◽  
Failure Modes ◽  
Urban Transport ◽  
Transport Systems ◽  
Centrality Measures ◽  
Complex Nature ◽  
Temporal Networks ◽  
World Systems ◽  
Temporal System ◽  
Spatio Temporal

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. To identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting spatio-temporally efficient flows through the network. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attacks.

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

Identifying important nodes based on upstream and downstream time-respecting paths in temporal networks

2021 ◽  
pp. 2150403
Author(s):  
Liang Luo ◽  
Minghao Li ◽  
Zili Zhang ◽  
Li Tao
Keyword(s):  
Real World ◽  
Social Contact ◽  
Centrality Measures ◽  
Temporal Networks ◽  
Contact Networks ◽  
Node Importance ◽  
Comparison Results ◽  
Temporal Structures ◽  
Social Contact Networks ◽  
The One

Identifying the nodes that play significant roles in the epidemic spreading process has attracted extensive attention in recent years. Few centrality measures, such as temporal degree and temporal closeness centrality, have been proposed to quantify node importance based on the topological structure of social contact networks. Most methods estimate the importance of a node from a single aspect, e.g. a higher degree in time snapshot graphs, or shorter distances to other nodes along time-respecting paths. However, this may not be the case in the real world. On the one hand, a node with more nodes on its out streams (i.e. downstream) should be more important because it may affect more nodes along its time-stamped contacting paths once it is infected. On the other hand, a node with more nodes in its in streams (i.e. upstream) deserves closer attention, as it has a higher probability of infection by other nodes. We propose a new temporal centrality measure, upstream and downstream centrality (UD-centrality) with two forms of realizations, i.e. a linear UD-centrality (L-UD) and a product UD-centrality (P-UD) to estimate the importance of nodes based on the temporal structures of social contact networks. We compare our L-UD and P-UD to three classic temporal network centralities through simulations on 14 real-world temporal networks based on the susceptible-infected (SI) model. The comparison results show that UD-centrality can more accurately rank the importance of nodes than the baseline centrality measures.

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.

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 Betweenness Centrality in Some Classes of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sunil Kumar Raghavan Unnithan ◽  
Balakrishnan Kannan ◽  
Madambi Jathavedan
Keyword(s):  
Real World ◽  
Betweenness Centrality ◽  
Shortest Paths ◽  
Centrality Measures ◽  
Flow Of Information

There are several centrality measures that have been introduced and studied for real-world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest paths between them. In this paper we present betweenness centrality of some important classes of graphs.

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