This paper studies the expressive power of graph neural networks falling within the
message-passing framework (GNNmp). Two results are presented. First, GNNmp are shown …

A hallmark of graph neural networks is their ability to distinguish the isomorphism class of
their inputs. This study derives hardness results for the classification variant of graph …

In the distributed subgraph detection problem, we are given a fixed subgraph H, and the
network must decide whether the network graph contains a copy of H or not. Subgraph …

We survey the recent distributed computing literature on checking whether a given
distributed system configuration satisfies a given boolean predicate, ie, whether the …

In this paper we give sublinear-time distributed algorithms in the CONGEST CONGEST
model for finding or listing cliques and even-length cycles. We show for the first time that all …

We present improved distributed algorithms for triangle detection and its variants in the
CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be …

A proof-labeling scheme (PLS) for a boolean predicate $\Pi $ on labeled graphs is a
mechanism used for certifying the legality with respect to $\Pi $ of global network states in a …

In this paper we present distributed property-testing algorithms for graph properties in the
CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P …

This is a survey of the exciting recent progress made in understanding the complexity of
distributed subgraph finding problems. It overviews the results and techniques for assorted …

We present simple deterministic algorithms for subgraph finding and enumeration in the
broadcast CONGEST model of distributed computation:--For any constant $ k $, detecting …