  Ordinary bond percolation (OP) can be viewed as a process where clusters grow
by joining them pairwise, by adding links chosen randomly one by one from a set
of predefined `virtual' links. In contrast, in agglomerative percolation (AP)
clusters grow by choosing randomly a `target cluster' and joining it with all
its neighbors, as defined by the same set of virtual links. Previous studies
showed that AP is in different universality classes from OP for several types
of (virtual) networks (linear chains, trees, Erdos-Renyi networks), but most
surprising were the results for 2-d lattices: While AP on the triangular
lattice was found to be in the OP universality class, it behaved completely
differently on the square lattice. In the present paper we explain this
striking violation of universality by invoking bipartivity. While the square
lattice is a bipartite graph, the triangular lattice is not. In conformity with
this we show that AP on the honeycomb and simple cubic (3-d) lattices -- both
of which are bipartite -- are also not in the OP universality classes. More
precisely, we claim that this violation of universality is basically due to a
Z_2 symmetry that is spontaneously broken at the percolation threshold. We also
discuss AP on bipartite random networks and suitable generalizations of AP on
k-partite graphs.
