We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.

翻译：我们描述并研究了一种基于传输的方法NetOTC（网络最优转移耦合），用于两个网络的比较与对齐。感兴趣的网络可具有有向或无向、加权或未加权特性，且顶点集规模可以不同。给定两个网络及其顶点间的成本函数，NetOTC通过寻找其关联随机游走的最优转移耦合实现期望成本最小化。该最小化成本量化了网络间的差异，而最优传输方案本身则提供了两个网络顶点与边的对齐。通过耦合完整随机游走（而非其边缘分布），NetOTC能够捕获网络的局部与全局信息，并保持边的完整性。该方法无需自由参数且不依赖随机化。我们研究了NetOTC的若干理论性质，并通过实验验证了其实证性能。