  Perturbative quantum field theories frequently feature rational linear
combinations of multiple zeta values (periods). In massless \phi^4-theory we
show that the periods originate from certain `primitive' vacuum graphs. Graphs
with vertex connectivity 3 are reducible in the sense that they lead to
products of periods with lower loop order. A new `twist' identity amongst
periods is proved and a list of graphs (the census) with their periods, if
available, is given up to loop order 8.
