I don’t think there are new cap[abilities in CVX 3.0beta for sparsity or chordal sparsity patterns. I don’t know whether there have been any improvements inside solvers callable from CVX, such as Mosek. A Mosek,developer, @Joachim_Dahl is co-author of “Linear matrix inequalities with chordal sparsity patterns andapplications to robust quadratic optimization” http://www.seas.ucla.edu/~vandenbe/publications/cacsd10.pdf
For info on changes in CVX 3.0beta vs. CVX 2.1, read the top text box at http://cvxr.com/cvx/beta/ and the links provided there.
The most significant changes can be found in the DCP ruleset section, due to the introduction of sign-sensitive convexity analysis.
Unfortunately, CVX 3.0beta is riddled with serious bugs, so use at your own peril.
One other thing CVX 3.0beta offers is the ability to use the native exponential cone capability of ECOS abd SCS. Unfortunately, the likelihood of encountering CXV 3.0beta bugs when trying to do so may negate this advantage. Also, CVXQUAD is now available for use under CVX, and that alows CVX;'s Successive Approximation method to be avoided - see CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions