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We examine 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. We argue that this is a natural metric for ranking nodes in a network, and we point out that it can be computed very rapidly even in the case of large networks. Furthermore, we propose(More)
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. In this paper we propose an extension of these measures to directed networks, and we apply them to the problem of ranking hubs and authorities. The extension is(More)
In a graph, a community may be loosely defined as a group of nodes that are more closely connected to one another than to the rest of the graph. One common theme is many formalizations is that flows should tend to stay within communities. Hence, we expect short cycles to play an important role. For undirected graphs, the importance of triangles – an(More)
We consider a broad class of walk-based, parameterized node centrality measures based on functions of the adjacency matrix. These measures generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be " tuned " to interpolate between degree and eigenvector centrality, which appear as limiting(More)
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present(More)
Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges(More)
This document contains details of numerical experiments performed to illustrate the theoretical results presented in our accompanying paper. 1. Limiting behavior of PageRank for small α. In this section we want to illustrate the behavior of the PageRank vector in the limit of small values of the parameter α. We take the following example from [8, pp.(More)