Let A[u,v] count graph edges with multiplicity. The functions chi_b(u)=(-1)^(b dot u) are an orthogonal basis: summing chi_b chi_c over all u is q when b=c and zero otherwise, by pairing one differing bit. Also A chi_b=chi_b sum_j (-1)^(b dot s_j). Thus the constant direction has eigenvalue d and every orthogonal direction has eigenvalue magnitude at most epsilon d. For vertex sets U,W, separate their indicator vectors into constant parts and zero-mean parts. The constant contribution to edge count is d|U||W|/q; Cauchy-Schwarz bounds the remaining contribution by epsilon d sqrt(|U||W|). Hence e(U,W)<=d|U||W|/q+epsilon d sqrt(|U||W|).