Heat flux distribution and rectification of complex networks

It was recently found that the heterogeneity of complex networks can enhance transport properties such as epidemic spreading, electric energy transfer, etc. A trivial deduction would be that the presence of hubs in complex networks can also accelerate the heat transfer although no concrete research has been done so far. In the present study, we have studied this problem and have found a surprising answer: the heterogeneity does not favor but prevents the heat transfer. We present a model to study heat conduction in complex networks and find that the network topology greatly affects the heat flux. The heat conduction decreases with the increase of heterogeneity of the network caused by both degree distribution and the clustering coefficient. Its underlying mechanism can be understood by using random matrix theory. Moreover, we also study the rectification effect and find that it is related to the degree difference of the network, and the distance between the source and the sink. These findings may have potential applications in real networks, such as nanotube/nanowire networks and biological networks.