This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon itself can be viewed more broadly as density or intensity function on networks, making the model a natural choice for comparison purposes. Extending graphon estimation towards modeling multiple networks simultaneously consequently provides substantial information about the (dis-)similarity between networks. Fitting such a joint model - which can be accomplished by applying an EM-type algorithm - provides a joint graphon estimate plus a corresponding prediction of the node positions for each network. In particular, it entails a generalized network alignment, where nearby nodes play similar structural roles in their respective domains. Given that, we construct a chi-squared test on equivalence of network structures. Simulation studies and real-world examples support the applicability of our network comparison strategy.

翻译：本文聚焦于基于统计推断的网络比较问题。为此，我们采用平滑图模型作为非参数建模策略，该模型能够捕捉复杂的结构模式。图模型本身可更广泛地视为网络的密度或强度函数，使其成为网络比较任务的天然选择。将图模型估计扩展至多网络联合建模，可有效揭示网络间的相似性与差异性。通过应用EM型算法拟合此类联合模型，可获得联合图模型估计及各网络节点位置的对应预测。特别地，该方法实现了广义网络对齐，其中邻近节点在各自领域中扮演相似的结构角色。基于此，我们构建了网络结构等价性的卡方检验。仿真实验和实际案例验证了所提网络比较策略的有效性。