  Summarizing web graphs is challenging due to the heterogeneity of the modeled
information and its changes over time. We investigate the use of neural
networks for lifelong graph summarization. Assuming we observe the web graph at
a certain time, we train the networks to summarize graph vertices. We apply
this trained network to summarize the vertices of the changed graph at the next
point in time. Subsequently, we continue training and evaluating the network to
perform lifelong graph summarization. We use the GNNs Graph-MLP and GraphSAINT,
as well as an MLP baseline, to summarize the temporal graphs. We compare
$1$-hop and $2$-hop summaries. We investigate the impact of reusing parameters
from a previous snapshot by measuring the backward and forward transfer and the
forgetting rate of the neural networks. Our extensive experiments on ten weekly
snapshots of a web graph with over $100$M edges, sampled in 2012 and 2022, show
that all networks predominantly use $1$-hop information to determine the
summary, even when performing $2$-hop summarization. Due to the heterogeneity
of web graphs, in some snapshots, the $2$-hop summary produces over ten times
more vertex summaries than the $1$-hop summary. When using the network trained
on the last snapshot from 2012 and applying it to the first snapshot of 2022,
we observe a strong drop in accuracy. We attribute this drop over the ten-year
time warp to the strongly increased heterogeneity of the web graph in 2022.
