Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and network flows. It is well-known that the topology of a network affects its resilience to failures or attacks, as well as its functions. Many real systems—such as the Internet, transportation networks and the brain—exchange information, so it is crucial to quantify how efficiently system’s units communicate. Measures of parallel communication efficiency for weighted networks rely on the identification of an ideal version of the system, which currently lacks a universal definition. Consequently, an inattentive choice might hinder a rigorous comparison of network flows across scales or might lead to a descriptor not robust to fluctuations in the topology or the flows. We propose a physically-grounded estimator of flow efficiency valid for any weighted network, regardless of scale, nature of weights and (missing) metadata, allowing for comparison across disparate systems. Our estimator captures the effect of flows heterogeneity along with topological differences of both synthetic and empirical systems. We also show that cutting the heaviest connections may increase the average efficiency of the system and hence, counterintuively, a sparser network is not necessarily less efficient.

网络科学能够有效分析真实的互连系统，其特点是拓扑和网络流之间的复杂相互作用。众所周知，网络的拓扑结构会影响其对故障或攻击的恢复能力及其功能。许多真实系统（例如互联网、交通网络和大脑）交换信息，因此量化系统单元的通信效率至关重要。加权网络并行通信效率的度量依赖于系统理想版本的识别，目前缺乏通用定义。因此，粗心的选择可能会阻碍跨尺度的网络流的严格比较，或者可能导致描述符对拓扑或流的波动不稳健。我们提出了一种基于物理的流效率估算器，适用于任何加权网络，无论规模、权重性质和（缺失）元数据如何，都允许跨不同系统进行比较。我们的估计器捕捉了流动异质性的影响以及合成和经验系统的拓扑差异。我们还表明，切断最重的连接可能会提高系统的平均效率，因此，与直觉相反，较稀疏的网络不一定效率较低。