Related papers: The Graph Pencil Method: Mapping Subgraph Densitie…
Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…
Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment…
We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical…
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…
We consider the spectral properties of balanced stochastic block models of which the average degree grows slower than the number of nodes (sparse regime) or proportional to it (dense regime). For both regimes, we prove a phase transition of…
We study sharp detection thresholds for degree corrections in Stochastic Block Models in the context of a goodness of fit problem, and explore the effect of the unknown community assignment (a high dimensional nuisance parameter) and the…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…
This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM),…
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
The stochastic block model (SBM) is a mixture model used for the clustering of nodes in networks. It has now been employed for more than a decade to analyze very different types of networks in many scientific fields such as Biology and…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
This paper proposes a novel scalable community-based neural framework for graph learning. The framework learns the graph topology through the task of community detection and link prediction by optimizing with our proposed joint SBM loss…
We asymptotically determine the maximum density of subgraphs isomorphic to $H$, where $H$ is any graph containing a dominating vertex, in graphs $G$ on $n$ vertices with bounded maximum degree and bounded clique number. That is, we…
Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…
The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special…