How about this?
function main_component(g)
c = connected_components(g)
_, i = findmax(length.(c))
g[c[i]]
end
julia> g = erdos_renyi(1000, 1000)
{1000, 1000} undirected simple Int64 graph
julia> main_component(g)
{802, 970} undirected simple Int64 graph