  The r-parity tensor of a graph is a generalization of the adjacency matrix,
where the tensor's entries denote the parity of the number of edges in
subgraphs induced by r distinct vertices. For r=2, it is the adjacency matrix
with 1's for edges and -1's for nonedges. It is well-known that the 2-norm of
the adjacency matrix of a random graph is O(\sqrt{n}). Here we show that the
2-norm of the r-parity tensor is at most f(r)\sqrt{n}\log^{O(r)}n, answering a
question of Frieze and Kannan who proved this for r=3. As a consequence, we get
a tight connection between the planted clique problem and the problem of
finding a vector that approximates the 2-norm of the r-parity tensor of a
random graph. Our proof method is based on an inductive application of
concentration of measure.
