Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network. Tree and branch decompositions considered here directly represent network structure as trees for recursive computation of network properties. Unlike coarse-graining approximations in terms of community structure or metapopulations, tree decompositions of sufficiently small width allow for exact results on equilibrium processes. Here we use simulated annealing to find tree decompositions of narrow width for a set of medium-size empirical networks. Rather than optimizing tree decompositions directly, we employ a search space constituted by so-called elimination orders being permutations on the network's node set. For each in a database of empirical networks with up to 1000 edges, we find a tree decomposition of low width.

中文翻译：

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模拟退火对现实网络的树分解

网络的分解不仅对结构探索有用。它们还对在给定网络上运行的进程（例如Ising模型，渗流，SIR模型）的分析和计算解决方案产生影响并使用它们。这里考虑的树和分支分解直接将网络结构表示为树，用于递归计算网络属性。与在群落结构或亚种群方面的粗粒度近似不同，宽度足够小的树木分解可以在平衡过程中获得准确的结果。在这里，我们使用模拟退火来为一组中等规模的经验网络找到窄宽度的树分解。与其直接优化树分解，不如使用由所谓消除顺序构成的搜索空间，这些消除顺序是网络上的排列。的节点集。对于具有多达1000条边的经验网络数据库中的每一个，我们都发现了低宽度的树分解。