Lots of zero entries in L factor found by chol and CHOLMOD

I have used Matlab's chol() and CHOLMOD for decomposing A into L and L'. I know that there will be fill-ins. However, L factor found by chol() has lots of very very small numbers. Number of zero entries in L factor found by CHOLMOD has lots of zero entries. I have run these two methods on a large set of symmetric positive definite sparse matrices from UFL. For instance, L factors of Muu matrix show the above-mentioned anomalies.

For Muu, there are 88.618 nonzeros in the lower triangular part of A. L factor found by CHOLMOD contains 239.912 entries. 186.826 entries are nonzero, remaining 53.086 are zero, which are explicitly stored in sparse data structures. L factor found by chol() contains 1.497.725 entries.

I used SuiteSparse/CHOLMOD/Demo/cholmod_demo.c source code for generating L factor.

I wonder why these zero entries exist in L? Is it correct to remove very very small numbers below a certain threshold or zero entries from L factors? What may be the threshold?