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Ordinary bond percolation (OP) can be viewed as a process where clusters growby joining them pairwise, by adding links chosen randomly one by one from a setof predefined `virtual' links. In contrast, in agglomerative percolation (AP)clusters grow by choosing randomly a `target cluster' and joining it with allits neighbors, as defined by the same set of virtual links. Previous studiesshowed that AP is in different universality classes from OP for several typesof (virtual) networks (linear chains, trees, Erdos-Renyi networks), but mostsurprising were the results for 2-d lattices: While AP on the triangularlattice was found to be in the OP universality class, it behaved completelydifferently on the square lattice. In the present paper we explain thisstriking violation of universality by invoking bipartivity. While the squarelattice is a bipartite graph, the triangular lattice is not. In conformity withthis we show that AP on the honeycomb and simple cubic (3-d) lattices -- bothof which are bipartite -- are also not in the OP universality classes. Moreprecisely, we claim that this violation of universality is basically due to aZ_2 symmetry that is spontaneously broken at the percolation threshold. We alsodiscuss AP on bipartite random networks and suitable generalizations of AP onk-partite graphs.

Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking