  Data breaches and ransomware attacks occur so often that they have become
part of our daily news cycle. This is due to a myriad of factors, including the
increasing number of internet-of-things devices, shift to remote work during
the pandemic, and advancement in adversarial techniques, which all contribute
to the increase in both the complexity of data captured and the challenge of
protecting our networks. At the same time, cyber research has made strides,
leveraging advances in machine learning and natural language processing to
focus on identifying sophisticated attacks that are known to evade conventional
measures. While successful, the shortcomings of these methods, particularly the
lack of interpretability, are inherent and difficult to overcome. Consequently,
there is an ever-increasing need to develop new tools for analyzing cyber data
to enable more effective attack detection. In this paper, we present a novel
framework based in the theory of hypergraphs and topology to understand data
from cyber networks through topological signatures, which are both flexible and
can be traced back to the log data. While our approach's mathematical grounding
requires some technical development, this pays off in interpretability, which
we will demonstrate with concrete examples in a large-scale cyber network
dataset. These examples are an introduction to the broader possibilities that
lie ahead; our goal is to demonstrate the value of applying methods from the
burgeoning fields of hypernetwork science and applied topology to understand
relationships among behaviors in cyber data.
