  Most research concerning the influence of network structure on phenomena
taking place on the network focus on relationships between global statistics of
the network structure and characteristic properties of those phenomena, even
though local structure has a significant effect on the dynamics of some
phenomena. In the present paper, we propose a new analysis method for phenomena
on networks based on a categorization of nodes. First, local statistics such as
the average path length and the clustering coefficient for a node are
calculated and assigned to the respective node. Then, the nodes are categorized
using the self-organizing map (SOM) algorithm. Characteristic properties of the
phenomena of interest are visualized for each category of nodes. The validity
of our method is demonstrated using the results of two simulation models. The
proposed method is useful as a research tool to understand the behavior of
networks, in particular, for the large-scale networks that existing
visualization techniques cannot work well.
