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Abstract

The K4 graph and the inertia of the adjacency matrix for a connected planar graph. A substantial history exists about incorporating matrix analysis and graph theory into geography and the geospatial sciences. This study contributes to that literature, aiding in analyses of spatial relationships, especially in terms of spatial weights matrices. We focus on the n-by-n 0ā€“1 binary adjacency matrix, whose rows and columns represent the nodes of a connected planar graph. The inertia of this matrix represents the number of positive (n+), negative (nāˆ’), and zero (n0) eigenvalues. Approximating the Jacobian term of spatial auto-normal models can benefit from calculating these matrix quantities. We establish restrictions for n- exploiting properties we uncover for the K4 graph.
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