Advancements in Graph Theory and Network Analysis

The field of graph theory and network analysis is currently experiencing significant developments, with a focus on improving the understanding and modeling of complex systems. Researchers are exploring new methods for analyzing and visualizing graph structures, including the use of geometric and topological techniques. The study of graph densities and extremal graph theory is also ongoing, with a particular emphasis on understanding the properties of $k$-planar graphs. Furthermore, there is a growing interest in the application of graph theory to real-world problems, such as network optimization and community detection. Noteworthy papers in this area include the introduction of a novel method for detecting anomalies in time-evolving simplicial complexes, which leverages the spectral properties of Hodge Laplacians to effectively model multi-way interactions among data points. Additionally, a new curvature metric for hypergraphs, called hypergraph lower Ricci curvature, has been proposed, which achieves a principled balance between interpretability and efficiency.

Sources

Cartesian Prime Graphs and Cospectral Families

A first view on the density of 5-planar graphs

HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection

Survey: Graph Databases

A Practical Linear Time Algorithm for Optimal Tree Decomposition of Halin Graphs

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures

UTCS: Effective Unsupervised Temporal Community Search with Pre-training of Temporal Dynamics and Subgraph Knowledge

Detecting Patterns of Interaction in Temporal Hypergraphs via Edge Clustering

Lower Ricci Curvature for Hypergraphs

Better Late than Never: the Complexity of Arrangements of Polyhedra

Compressing Hypergraphs using Suffix Sorting

The Peculiarities of Extending Queue Layouts

Built with on top of