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The principal eigenvector x1 belonging to the largest adjacency Eigen value (i.e. The spectral radius) of a graph is one of the most popular centrality metrics. The spectral radius of the adjacency matrix powerfully characterizes the dynamic processes on networks, such as virus spread and synchronization. The sum of components of the principal eigenvector, which is also called the fundamental weight...
Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions...
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