Asymptotics for the size of the largest component scaled to log n
in inhomogeneous random graphs
Tatyana S. Turova
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2008
ISSN 14039338

Abstract:

We study the inhomogeneous random graphs in the subcritical case. We derive
an exact formula for the size of the largest connected component scaled to
log n where n is the size of the graph. This generalizes the
recent result for the "rank 1 case". In particular, here we discover that
the same wellknown equation for the survival probability, whose positive
solution determines the asymptotics of the size of the largest component
in the supercritical case, plays the crucial role in the subcritical case
as well. But now these are the negative solutions which come into
play.





