  By introducing a simple competition mechanism for bond insertion in random
graphs, explosive percolation exhibits a sharp phase transition with rich
critical phenomena. We investigate high-order connectivity in explosive
percolation using an event-based ensemble, focusing on biconnected clusters,
where any two sites are connected by at least two independent paths. Our
numerical analysis confirms that explosive percolation with different
intra-cluster bond competition rules shares the same percolation threshold and
universality, with biconnected clusters percolating simultaneously with simply
connected clusters. However, the volume fractal dimension $d_{f}'$ of
biconnected clusters varies depending on the competition rules of intra-cluster
bonds. The size distribution of biconnected clusters exhibits double-scaling
behavior: large clusters follow the standard Fisher exponent derived from the
hyperscaling relation $\tau'=1+1/d_{f}'$, while small clusters display a
modified Fisher exponent $\tau_0<\tau'$. These findings provide insights into
the intricate nature of connectivity in explosive percolation.
