  We revisit the problem of counting the number of copies of a fixed graph in a
random graph or multigraph, including the case of constrained degrees. Our
approach relies heavily on analytic combinatorics and on the notion of
patchwork to describe the possible overlapping of copies.
  This paper is a version, extended to include proofs, of the paper with the
same title to be presented at the Eurocomb 2017 meeting.
