  Goodman proved that the sum of the number of triangles in a graph on $n$
nodes and its complement is at least $n^3/24$; in other words, this sum is
minimized, asymptotically, by a random graph with edge density $1/2$. Erd\H{o}s
conjectured that a similar inequality will hold for $K_4$ in place of $K_3$,
but this was disproved by Thomason. But an analogous statement does hold for
some other graphs, which are called {\it common graphs}. A characterization of
common graphs seems, however, out of reach.
  Franek and R\"odl proved that $K_4$ is common in a weaker, local sense. Using
the language of graph limits, we study two versions of locally common graphs.
We sharpen a result of Jagger, \v{S}tov\'{\i}\v{c}ek and Thomason by showing
that no graph containing $K_4$ can be locally common, but prove that all such
graphs are weakly locally common. We also show that not all connected graphs
are weakly locally common.
