  Community Search (CS) is one of the fundamental graph analysis tasks, which
is a building block of various real applications. Given any query nodes, CS
aims to find cohesive subgraphs that query nodes belong to. Recently, a large
number of CS algorithms are designed. These algorithms adopt predefined
subgraph patterns to model the communities, which cannot find ground-truth
communities that do not have such pre-defined patterns in real-world graphs.
Thereby, machine learning (ML) and deep learning (DL) based approaches are
proposed to capture flexible community structures by learning from ground-truth
communities in a data-driven fashion. These approaches rely on sufficient
training data to provide enough generalization for ML models, however, the
ground-truth cannot be comprehensively collected beforehand.
  In this paper, we study ML/DL-based approaches for CS, under the circumstance
of small training data. Instead of directly fitting the small data, we extract
prior knowledge which is shared across multiple CS tasks via learning a meta
model. Each CS task is a graph with several queries that possess corresponding
partial ground-truth. The meta model can be swiftly adapted to a task to be
predicted by feeding a few task-specific training data. We find that trivially
applying multiple classical metalearning algorithms to CS suffers from problems
regarding prediction effectiveness, generalization capability and efficiency.
To address such problems, we propose a novel meta-learning based framework,
Conditional Graph Neural Process (CGNP), to fulfill the prior extraction and
adaptation procedure. A meta CGNP model is a task-common node embedding
function for clustering, learned by metric-based graph learning, which fully
exploits the characteristics of CS. We compare CGNP with CS algorithms and ML
baselines on real graphs with ground-truth communities.
