  Viral information like rumors or fake news is spread over a communication
network like a virus infection in a unidirectional manner: entity $i$ conveys
information to a neighbor $j$, resulting in two equally informed (infected)
parties. Existing graph diffusion works focus only on bidirectional diffusion
on an undirected graph. Instead, we propose a new directed acyclic graph (DAG)
diffusion model to estimate the probability $x_i(t)$ of node $i$'s infection at
time $t$ given a source node $s$, where $x_i(\infty)~=~1$. Specifically, given
an undirected positive graph modeling node-to-node communication, we first
compute its graph embedding: a latent coordinate for each node in an assumed
low-dimensional manifold space from extreme eigenvectors via LOBPCG. Next, we
construct a DAG based on Euclidean distances between latent coordinates.
Spectrally, we prove that the asymmetric DAG Laplacian matrix contains real
non-negative eigenvalues, and that the DAG diffusion converges to the
all-infection vector $\x(\infty) = \1$ as $t \rightarrow \infty$. Simulation
experiments show that our proposed DAG diffusion accurately models viral
information spreading over a variety of graph structures at different time
instants.
