Title: A playful note on spanning and surplus edges,
Abstract: Consider a (not necessarily near-critical) random graph running in continuous
time. A recent breadth-first-walk construction is extended in order to account
for the surplus edge data in addition to the spanning edge data. Two different
graph representations of the multiplicative coalescent, with different
advantages and drawbacks, are discussed in detail. A canonical multi-graph of
Bhamidi, Budhiraja and Wang (2014) naturally emerges. The presented framework
should facilitate understanding of scaling limits with surplus edges for
near-critical random graphs in the domain of attraction of general (not
necessarily standard) eternal multiplicative coalescent.