Related papers: Graphlet decomposition of a weighted network

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…

We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…

In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…

Graph representation learning has recently been applied to a broad spectrum of problems ranging from computer graphics and chemistry to high energy physics and social media. The popularity of graph neural networks has sparked interest, both…

An essential goal in mechanistic interpretability to decode a network, i.e., to convert a neural network's raw weights to an interpretable algorithm. Given the difficulty of the decoding problem, progress has been made to understand the…

Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…

Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…

Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined…

Despite the wide application of Graph Convolutional Network (GCN), one major limitation is that it does not benefit from the increasing depth and suffers from the oversmoothing problem. In this work, we first characterize this phenomenon…

Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…

We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…

We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local…

In this paper, we propose a new method to compute the barycenter of large weighted graphs endowed with probability measures on their nodes. We suppose that the edge weights are distances between the nodes and that the probability measure on…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…