Related papers: Discrete Hyperbolic Random Graph Model
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is…
This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data.…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Real-world graphs are typically complex, exhibiting heterogeneity in the global structure, as well as strong heterophily within local neighborhoods. While a growing body of literature has revealed the limitations of common graph neural…
We provide new connectivity results for {\em vertex-random graphs} or {\em random annulus graphs} which are significant generalizations of random geometric graphs. Random geometric graphs (RGG) are one of the most basic models of random…
Graph neural network (GNN) has shown superior performance in dealing with graphs, which has attracted considerable research attention recently. However, most of the existing GNN models are primarily designed for graphs in Euclidean spaces.…
Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
Networks are one of the most valuable data structures for modeling problems in the real world. However, the most recent node embedding strategies have focused on undirected graphs, with limited attention to directed graphs, especially…
Heterogeneous graphs (HGs) are common in real-world scenarios and often exhibit heterophily. However, most existing studies focus on either heterogeneity or heterophily in isolation, overlooking the prevalence of heterophilic HGs in…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
We introduce Hyperdimensional Graph Learner (HDGL), a novel method for node classification and link prediction in graphs. HDGL maps node features into a very high-dimensional space (\textit{hyperdimensional} or HD space for short) using the…
To leverage the complex structures within heterogeneous graphs, recent studies on heterogeneous graph embedding use a hyperbolic space, characterized by a constant negative curvature and exponentially increasing space, which aligns with the…
This paper examines mathematical models for processing classical horizontal geodetic (triangulation and trilateration) networks. Two rigorous parametric adjustment models are discussed. The first one is a well-known model of adjustment in…
Hyperbolic geometry offers a natural focus + context for data visualization and has been shown to underlie real-world complex networks. However, current hyperbolic network visualization approaches are limited to special types of networks…
Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex…
Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only…
Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…