Inequalities between subgraph densities carries interesting information about
graphs. One example of such information is how close a graphs 4-cycle density
is to its edge density tells us how ’random’ a graph looks. We will discuss how
subgraph densities can be expressed as an integral of multivariate functions
taken to the appropriate root. These integrals are generalization of Lp norms,
which motivates the question of when subgraph densities are also norms. One
result of Hatamis paper is to show that all hypercube densities are a norm,
which then allows us to apply functional analytic tools to derive inequalities
between subgraph densities. We will prove that hypercube densities are
norms in this talk.