Related papers: Sampling Random Graphs from the Colored Configurat…

We introduce Polaris, a network null model for colored multi-graphs that preserves the Joint Color Matrix. Polaris is specifically designed for studying network polarization, where vertices belong to a side in a debate or a partisan group,…

Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of…

Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes…

We develop a new method to efficiently sample synthetic networks that preserve the d-hop neighborhood structure of a given network for any given d. The proposed algorithm trades off the diversity in network samples against the depth of the…

Consider a graph G with n nodes and m edges, which represents a social network, and assume that initially each node is blue or white. In each round, all nodes simultaneously update their color to the most frequent color in their…

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the…

Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…

Formula recognition presents significant challenges due to the complicated structure and varied notation of mathematical expressions. Despite continuous advancements in formula recognition models, the evaluation metrics employed by these…

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have…

Networks and data supported on graphs have become ubiquitous in the sciences and engineering. This paper studies the 'blind' community detection problem, where we seek to infer the community structure of a graph model given the observation…

Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$…

One of the essential issues in decision problems and preference modeling is the number of comparisons and their pattern to ask from the decision maker. We focus on the optimal patterns of pairwise comparisons and the sequence including the…

The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…

Deep semantic matching aims to discriminate the relationship between documents based on deep neural networks. In recent years, it becomes increasingly popular to organize documents with a graph structure, then leverage both the intrinsic…

The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…

Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…

In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and…

Learners sharing similar implicit cognitive states often display comparable observable problem-solving performances. Leveraging collaborative connections among such similar learners proves valuable in comprehending human learning. Motivated…

In many real-world applications such as social network analysis, knowledge graph discovery, biological network analytics, and so on, graph data management has become increasingly important and has drawn much attention from the database…

Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not…