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Thus, our proposed LCCDC metric is significantly different from that of the leverage centrality, closeness centrality, and the other centrality metrics.
Hence, the leverage centrality metric cannot be a suitable alternate for the betweenness centrality (BWC) metric, as is also evidenced in the correlation studies of [39]: the correlation between leverage centrality and BWC is lower than the correlation between degree centrality and BWC.
Among the various localized centrality metrics proposed in the literature, the "leverage" centrality metric proposed by Joyce et al. [39] for brain networks has gained prominence. Leverage centrality of a node is a measure of the extent of connectivity of the node relative to the connectivity of its neighbors.
Leverage centrality is based on the notion that a node with degree higher than the degree of its neighbors is likely to be more influential on its neighbors and vice-versa.
For a node i with degree (k_{i}) and set of neighbors (N_{i}), the leverage centrality of node i, LVC((i =frac{1}{k_i }sum nolimits _{jin N_i } {frac{k_i -k_j }{k_i +k_j }} ) [39].
Moreover, the above formulation for leverage centrality metric compares the degree of a node with the degree of an individual neighbor node, and fails to take into consideration the connectivity among the neighbor nodes themselves (without involving the node in consideration).
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Although leverage and eigenvector centrality are both derivatives of degree centrality, clearly these metrics do not convey the same information.
The analysis revealed a significant difference between leverage and eigenvector centrality (p = 0.021), while the difference between degree and eigenvector centrality was only marginally significant (p = 0.06).
A 3-dimensional plot of eigenvector, leverage, and degree centrality revealed that the group of nodes below the synthetic network data in Figure 5 in fact consisted of two subgroups (Figure 6A).
Scatter plots of the degree, leverage, betweenness, and eigenvector centrality were created for the brain networks of all subjects.
Degree, leverage, betweenness, and eigenvector centrality were examined as an additional axis to a functional cartography plot to compare the metrics' abilities to identify hubs in brain networks.
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