On the Limiting Behavior of Parameter-Dependent Network Centrality Measures

@article{Benzi2015OnTL,
  title={On the Limiting Behavior of Parameter-Dependent Network Centrality Measures},
  author={Michele Benzi and Christine Klymko},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2015},
  volume={36},
  pages={686-706}
}
We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including Katz and subgraph centralities. We show that the parameter can be “tuned" to interpolate between degree and eigenvector centralities, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained… Expand
Matching exponential-based and resolvent-based centrality measures
TLDR
It is argued that the centralities computed in floating point arithmetic can nevertheless reliably be used for ranking and shown that the new choice of Katz parameter leads to rankings of nodes that match those from the exponential centralities well in practice. Expand
A General Centrality Framework-Based on Node Navigability
TLDR
The Potential Gain is introduced as a centrality measure that unifies many walk-based centrality metrics in graphs and captures the notion of node navigability, interpreted as the property of being reachable from anywhere else (in the graph) through short walks. Expand
Influence measures in subnetworks using vertex centrality
TLDR
A decomposition of the relative centrality measure is given, by including also the relative influence of the single node with respect to a given subgraph containing it, in both the entire network and the specific sectors to which the assets belong. Expand
The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis
TLDR
A new network centrality measure based on the concept of nonbacktracking walks, that is, walks not containing subsequences of the form uvu where u and v are any distinct connected vertices of the underlying graph, is introduced and studied. Expand
Subgraph centrality and walk-regularity
TLDR
This work considers when non--walk-regular graphs can achieve maximum entropy, calling such graphs $\textit{entropic}$, and builds infinite families of entropic graphs, as well as a family of witnessing parameters with a limit point at zero. Expand
Eigenvector-Based Centrality Measures for Temporal Networks
TLDR
This paper applies a principled generalization of network centrality measures that is valid for any eigenvector-based centrality to three empirical temporal networks, and introduces the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. Expand
Localization of eigenvector centrality in networks with a cut vertex.
  • K. Sharkey
  • Medicine, Mathematics
  • Physical review. E
  • 2019
We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cutExpand
Gaussianization of the spectra of graphs and networks. Theory and applications
Abstract Matrix functions of the adjacency matrix are very useful for understanding important structural properties of graphs and networks, such as communicability, node centrality, bipartivity, andExpand
Centrality Measures for Graphons: Accounting for Uncertainty in Networks
TLDR
A statistical approach based on graphon theory is suggested: formal definitions of centrality measures for graphons are introduced and their connections to classical graph centralities measures are established, demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size. Expand
Analysis of directed networks via the matrix exponential
TLDR
Some methods to identify important nodes in a directed network using the matrix exponential are discussed, taking into account that the notion of importance changes whether the authors consider the influence of a given node along the edge directions or how it is influenced by directed paths that point to it (upstream influence). Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 72 REFERENCES
A Parameterized Centrality Metric for Network Analysis
  • Rumi Ghosh, Kristina Lerman
  • Mathematics, Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
TLDR
A normalized version of alpha-centrality is introduced and used to study network structure, for example, to rank nodes and find community structure of the network and it is shown that it leads to better insights into network structure than alternative metrics. Expand
Total communicability as a centrality measure
TLDR
A node centrality measure based on the notion of total communicability, defined in terms of the row sums of the exponential of the adjacency matrix of the network, is examined and the total sum of node communicabilities is proposed as a useful measure of network connectivity. Expand
Subgraph centrality in complex networks.
TLDR
A new centrality measure that characterizes the participation of each node in all subgraphs in a network, C(S)(i), which is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness, and eigenvector centralities. Expand
Correlations among centrality measures in complex networks
In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centralityExpand
Ranking hubs and authorities using matrix functions
TLDR
The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks and are applied to directed networks, leading to a technique for ranking hubs and authorities. Expand
Local estimates for eigenvector-like centralities of complex networks
  • M. Romance
  • Computer Science, Mathematics
  • J. Comput. Appl. Math.
  • 2011
TLDR
Several centrality measures are analyzed by giving a general framework that includes the Bonacich centrality, PageRank centrality or in-degree vector, among others, by giving some geometrical characterizations and some deviation results that help to quantify the error of approximating a spectral centrality by a local estimator. Expand
Network Properties Revealed through Matrix Functions
TLDR
A general class of measures based on matrix functions is introduced, and it is shown that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments. Expand
Analyzing complex networks through correlations in centrality measurements
TLDR
It is shown that the centralities are in general correlated, but with stronger correlations for network models than for real networks, and that the use of a centrality correlation profile, consisting of the values of the correlation coefficients between all pairs of centralities of interest, as a way to characterize networks. Expand
Centrality and Communicability Measures in Complex Networks: Analysis and Algorithms
TLDR
An analytical relationship between these rankings and the degree and subgraph centrality rankings is demonstrated, which helps to explain the observed robustness of these rankings on many real world networks, even though the scores produced by the centrality measures are not stable. Expand
Spectral scaling and good expansion properties in complex networks
The existence of a scaling between the principal eigenvector and the subgraph centrality of a complex network indicates that the network has "good expansion" (GE) properties. GE is the important butExpand
...
1
2
3
4
5
...