Article ID Journal Published Year Pages File Type
7378235 Physica A: Statistical Mechanics and its Applications 2016 8 Pages PDF
Abstract
The eigenvalues and eigenvectors of the adjacency matrix of a network contain essential information about its topology. For each of the Chinese language co-occurrence networks constructed from four literary genres, i.e., essay, popular science article, news report, and novel, it is found that the largest eigenvalue depends on the network size N, the number of edges, the average shortest path length, and the clustering coefficient. Moreover, it is found that their node-degree distributions all follow a power-law. The number of different eigenvalues, Nλ, is found numerically to increase in the manner of Nλ∝logN for novel and Nλ∝N for the other three literary genres. An “M” shape or a triangle-like distribution appears in their spectral densities. The eigenvector corresponding to the largest eigenvalue is mostly localized to a node with the largest degree. For the above observed phenomena, mathematical analysis is provided with interpretation from a linguistic perspective.
Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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