Simple and unbiased kernel function for network analysis

This paper proposes a new kernel function on networks which has desired properties for the analysis of density of event occurances on the networks. Our proposal is an extension of an existing kernel function called the equal-split kernel function. This function is simple, but is valid only when the lengths of all the cycles are larger than the width of the support of the kernel function. In this paper, we modify the equal-split kernel function in such a way that the unbiasedness is guaranteed even if the network contains shorter cycles.