We study network properties of networks evolving in time based on optimal transport principles. These evolve from a structure covering uniformly a continuous space towards an optimal design in terms of optimal transport theory. At convergence, the networks should optimize the way resources are transported through it. As the network structure shapes in time towards optimality, its topological properties also change with it. The question is how do these change as we reach optimality. We study the behavior of various network properties on a number of network sequences evolving towards optimal design and find that the transport cost function converges earlier than network properties and that these monotonically decrease. This suggests a mechanism for designing optimal networks by compressing dense structures. We find a similar behavior in networks extracted from real images of the networks designed by the body shape of a slime mold evolving in time.

翻译：我们根据最佳运输原则研究在时间上演变的网络的网络特性,这些特性从一个统一覆盖连续空间的结构演变成一个最佳运输理论的最佳设计。在趋同时,网络应该优化资源通过它运输的方式。随着网络结构的形成,其地形特性也会随着它的变化而变化。当我们达到最佳性能时,这些变化是如何发生的。我们研究各种网络特性在一系列网络序列上的行为,这些网络特性正在向最佳设计演变,发现运输成本功能比网络特性早于网络特性,而且这种单质下降。这表明了通过压缩密度结构来设计最佳网络的机制。我们在从由薄质模型体形设计的网络的真实图像中发现了类似的行为。