  As an intuitive description of complex physical, social, or brain systems,
complex networks have fascinated scientists for decades. Recently, to abstract
a network's structural and dynamical attributes for utilization, network
representation has been one focus, mapping a network or its substructures (like
nodes) into a low-dimensional vector space. Since the current methods are
mostly based on machine learning, a black box of an input-output data fitting
mechanism, generally the space's dimension is indeterminable and its elements
are not interpreted. Although massive efforts to cope with this issue have
included, for example, automated machine learning by computer scientists and
computational theory by mathematics, the root causes still remain unresolved.
Given that, from a physical perspective, this article proposes two determinable
and interpretable node representation methods. To evaluate their effectiveness
and generalization, this article further proposes Adaptive and Interpretable
ProbS (AIProbS), a network-based model that can utilize node representations
for link prediction. Experimental results showed that the AIProbS can reach
state-of-the-art precision beyond baseline models, and by and large it can make
a good trade-off with machine learning-based models on precision, determinacy,
and interpretability, indicating that physical methods could also play a large
role in the study of network representation.
