Such filtered graphs and their clique complexes correspond to the filtered Vietoris-Rips complex commonly used in topological data analysis. The mathematical foundations regarding the compatibility of ...

Recent investigations have advanced the theory of geometric intersection graphs by elucidating the relationship between their structural properties and chromatic number.

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A previous version of this paper, entitled 'Expander Flows, Geometric Embeddings, and Graph Partitioning," was published in Proceedings of the 36th Annual Symposium on the Theory of Computing (Chicago ...

In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a ...

Mathematicians have long sought to develop algorithms that can compare any two graphs. In practice, many ...

Random Graphs Graph Theory and Quantum Probability Geometric Graph Processes Probability on Algebraic Structures: Time-Homogeneous Random Walks Dynamic Walks in Clifford Algebras Iterated Stochastic ...