This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient, such as in Exponential random graphical models (ERGMs) and Markov networks, we construct a finite measure space with measure ratio statistics. A new performance measure of detection delay is proposed to detect the changes in distribution of the network. And an optimal sequential test is proposed under the performance measure. The good performance of the optimal sequential test is illustrated numerically on ERGMs and Erdos-R\'{e}nyi network sequences.

翻译：本文件考虑了网络有限序列的变化点问题。 为了避免在指数随机图形模型(ERGMS)和Markov网络中难以计算正常化系数, 我们用测量比率统计来构建一个有限的测量空间。 提议了一种新的检测延迟性能测量, 以检测网络分布的变化。 在性能测量下建议了最佳的顺序测试。 最佳顺序测试的良好性能在ERGMS 和 Erdos- R\' {e}nyi 网络序列中用数字说明。