  We study the effect of the network topology to propagation phenomena on
networks in this article. We do not assume any propagation model such as the
contact process or SIR model\cite{Ker} because the study is only the
consideratons of the purely topological effect, especially the effect of cycles
of a network. To uncover universal properties independent of explicit
propagation models is expected due to it. First of all, we introduce some
indeces for propagation phenomena of a network. Second we introduce a concept
of cycles with a little differences to usal cycles, which is called "STOC" in
the body of this article. We find some analytic relations between thesm, STOC
and some indeces. Moreover we can find the total number of STOCs in a network,
analytically. This consideration leads to an extension of the celebrated
"Euler's polyhedron formula", which is only applicable to planar graphs. This
extended formula is applicable to any graphs. Last we estimate numerically the
indeces and the number of STOCs based on the theoretical considerations for
some complex networks and make some discussion on the effects of cycles in
networks to propagation.
