  In \cite{Elek} we proved that the limit of a weakly convergent sequence of
finite graphs can be viewed as a graphing or a continuous field of infinite
graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph
sequences. We show that in this case the integrated density of states exists
that is the weak limit of the spectra of the graph Laplacians of the finite
graphs is the KNS-spectral measure of the graph Laplacian of the limit
graphing. Using this limit technique we prove a Cheeger type inequality for
finite graphs.
