We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs generated by the model densify over time. In the special case of the cone model, generated graphs provably satisfy properties observed in real-world complex networks such as the small world property and bad spectral expansion. We finish with a set of open problems and next steps for the frustum model.
翻译:我们考虑的是一个复杂网络的新模式,其基本机制是扩展密度子集。在丰厚的模型中,我们反复将晶体扩展至离散时间步骤。对于基础参数的许多选择,模型生成的图形会随着时间的推移而变密度。在锥形模型的特殊情况下,生成的图形可以明显地满足在现实世界复杂网络中观察到的特性,例如世界地产小和光谱扩展不良。我们用一系列开放的问题和丰度模型的下一步来结束。