## Conclusion and Discussion

We have studied the structural properties of the yeast protein interaction networks and the transport phenomena along the shortest pathways on biocomplex networks from the graph theoretic viewpoint. Thanks to recent development of data collection and graph analysis methods, the structural properties of the yeast protein interaction networks have been unveiled rapidly. Here we analyzed the degree distribution, the degree-degree correlation, and the clustering coefficient of the yeast interaction networks for several different datasets available9,24'25,27'31 and also for an integrated data we constructed. The yeast PIN is found to be strongly dissortative and highly modular. We believe that such analysis could be helpful for understanding the evolution of the protein interaction networks and finding protein interactions yet undiscovered. Moreover, we investigate the transport problem along the shortest pathways on biocomplex networks such as metabolic networks. We found that the load distribution follows a power law, and its exponent is robust, insensitive to detailed structural properties. We could classify real-world networks into two classes based on this property and also on the topological features of the shortest pathways. In particular, we find the metabolic networks for archaea belongs to the different class from that for bacteria and eukaryotes. The shortest pathway structure is simple for archaea. While further theoretical understandings are needed in relation to the robustness of the load distribution, at the moment, it would be interesting to notice that the load distribution is closely related to the structure of the core part of biocomplex networks.

Acknowledgement

This work is supported by the KOSEF Grant No. R14-2002-059-01000-0 in the ABRL program.

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