  Graph theoretical approach has proved an effective tool to understand,
characterize and quantify the complex brain network. However, much less
attention has been paid to methods that quantitatively compare two graphs, a
crucial issue in the context of brain networks. Comparing brain networks is
indeed mandatory in several network neuroscience applications. Here, we discuss
the current state of the art, challenges, and a collection of analysis tools
that have been developed in recent years to compare brain networks. We first
introduce the graph similarity problem in brain network application. We then
describe the methodological background of the available metrics and algorithms
of comparing graphs, their strengths and limitations. We also report results
obtained in concrete applications from normal brain networks. More precisely,
we show the potential use of brain network similarity to build a 'network of
networks' that may give new insights into the object categorization in the
human brain. Additionally, we discuss future directions in terms of network
similarity methods and applications.
