We call a graph \(G\) \( (p, \alpha ) \) jumbled if, for every induced subgraph \( H \) of \(G\) , \( | e(H)-p \binom {|H|} 2 | \leq \alpha |H| \) holds; here \(p\) and \(\alpha\) are real numbers with \( 0 < p <1 \leq \alpha, \) and \(e(H)\) is the number of edges in \(H\). We show that a \( (p, \alpha)-\) jumbleed graph behaves in many ways like a random graph with edge probability \(p\), and some aspects of this similarity are examined.

• Any \(k\)-regular graph, say \(k \sim \sqrt n\), with the second largest eigenvalue less the \(0.9 k\) but greater than \(0.8 k\) satisfies some neighborhood expansion property via Cheeger's inequality. However such a graph definitely does not satisfy the eigenvalue property, i.e., an eigenvalue upper bound \( \epsilon k \), which is one of the quasirandom properties.