  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.
