  Motivated by understanding the dynamics of sensitive social networks over
time, we consider the problem of continual release of statistics in a network
that arrives online, while preserving privacy of its participants. For our
privacy notion, we use differential privacy -- the gold standard in privacy for
statistical data analysis. The main challenge in this problem is maintaining a
good privacy-utility tradeoff; naive solutions that compose across time, as
well as solutions suited to tabular data either lead to poor utility or do not
directly apply. In this work, we show that if there is a publicly known upper
bound on the maximum degree of any node in the entire network sequence, then we
can release many common graph statistics such as degree distributions and
subgraph counts continually with a better privacy-accuracy tradeoff.
  Code available at https://bitbucket.org/shs037/graphprivacycode
