  The creation of social ties is largely determined by the entangled effects of
people's similarities in terms of individual characters and friends. However,
feature and structural characters of people usually appear to be correlated,
making it difficult to determine which has greater responsibility in the
formation of the emergent network structure. We propose \emph{AN2VEC}, a node
embedding method which ultimately aims at disentangling the information shared
by the structure of a network and the features of its nodes. Building on the
recent developments of Graph Convolutional Networks (GCN), we develop a
multitask GCN Variational Autoencoder where different dimensions of the
generated embeddings can be dedicated to encoding feature information, network
structure, and shared feature-network information. We explore the interaction
between these disentangled characters by comparing the embedding reconstruction
performance to a baseline case where no shared information is extracted. We use
synthetic datasets with different levels of interdependency between feature and
network characters and show (i) that shallow embeddings relying on shared
information perform better than the corresponding reference with unshared
information, (ii) that this performance gap increases with the correlation
between network and feature structure, and (iii) that our embedding is able to
capture joint information of structure and features. Our method can be relevant
for the analysis and prediction of any featured network structure ranging from
online social systems to network medicine.
