It is known from experiments that in the presence of soluble antigen, B-cell receptors (BCRs) assemble into microclusters and then collect into a macrocluster known as a 'cap'. However, the mechanisms of BCR cluster formation during recognition of soluble antigens remain unclear. In previous work, we demonstrated that effective intrinsic attractions among BCRs can lead to the formation of small microclusters of BCR molecules. The effective intrinsic attractions could be caused by multivalent antigen binding, association with lipid rafts, or other biochemical factors. In the present study, we have developed and studied a Monte Carlo model of BCR clustering mediated by explicit binding and crosslinking of soluble bivalent antigens. Antigen crosslinking is shown to microcluster BCRs in an affinity-dependent manner and also in a biologically relevant timescale; however, antigen crosslinking alone does not appear to be sufficient for the formation of a single macrocluster of receptor molecules. We show that directed transport of BCRs is needed to drive the formation of large macroclusters. We constructed a simple model of directed transport, where BCR molecules diffuse towards the largest cluster or towards a random BCR microcluster, which results in a single macrocluster of receptor molecules. The mechanisms for both types of directed transport are compared using network-based metrics. We also develop and use appropriate network measures to analyze the effect of BCR and antigen concentration on BCR clustering, the stability of the formed clusters over time and the size of BCR-antigen crosslinked chains.