Related papers: Relaxation-based coarsening and multiscale graph o…
We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
Convexification techniques have gained increasing interest over the past decades. In this work, we apply a recently developed convexification technique for fractional programs by He, Liu and Tawarmalani (2024) to the problem of determining…
Graph modification problems with the goal of optimizing some measure of a given node's network position have a rich history in the algorithms literature. Less commonly explored are modification problems with the goal of equalizing…
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…
We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…
We propose a novel iterative method to adapt a a graph to d-dimensional image data. The method drives the nodes of the graph towards image features. The adaptation process naturally lends itself to a measure of feature saliency which can…
The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…
Scalability of Graph Neural Networks (GNNs) remains a significant challenge. To tackle this, methods like coarsening, condensation, and computation trees are used to train on a smaller graph, resulting in faster computation. Nonetheless,…
Accessibility, defined as travel impedance between spatially dispersed opportunities for activity, is one of the main determinants of public transport use. In-depth understanding of its properties is crucial for optimal public transport…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
We adapt multilevel, force-directed graph layout techniques to visualizing dynamic graphs in which vertices and edges are added and removed in an online fashion (i.e., unpredictably). We maintain multiple levels of coarseness using a…