  Diffusion models simulate the propagation of influence in networks. The
design and evaluation of diffusion models has been subjective and empirical.
When being applied to a network represented by a graph, the diffusion model
generates a sequence of edges on which the influence flows, such sequence forms
a temporal network. In most scenarios, the statistical properties or the
characteristics of a network are inferred by analyzing the temporal networks
generated by diffusion models. To analyze real temporal networks, the motif has
been proposed as a reliable feature. However, it is unclear how the network
topology and the diffusion model affect the motif feature of a generated
temporal network. In this paper, we adopt the motif feature to evaluate the
temporal graph generated by a diffusion model, thence the diffusion model
itself. Two benchmarks for quantitively evaluating diffusion models with motif,
stability and separability, are proposed and measured on numerous diffusion
models. One motif-based metric is proposed to measure the similarity between
diffusion models. The experiments suggest that the motif of a generated
temporal network is dominated by the diffusion model, while the network
topology is almost ignored. This result indicates that more practical and
reliable diffusion models have to be designed with delicacy in order to capture
the propagation patterns of real temporal networks.

Social and Information Networks;Networking and Internet Architecture