Spectral Methods for Bisecting Graphs
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Gary Froyland * and Eric Kwok Partitions of networks that are robust to vertex permutation dynamics
Abstract:Minimumdisconnecting cuts of connected graphs provide fundamental information about the connectivity structure of the graph. Spectral methods are well-known as stable and efficient means of finding good solutions to the balanced minimum cut problem. In this paper we generalise the standard balanced bisection problem for static graphs to a new “dynamic balanced bisection problem”, in wh...
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Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...
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