We study the merging process when Kruskal's algorithm is run with random graphs as inputs. Our aim is to analyze this process when the underlying graph is the complete graph ...
We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte...
Constructing a good graph to represent data structures is critical for many important machine learning tasks such as clustering and classification. This paper proposes a novel no...
Liansheng Zhuang, Haoyuan Gao, Zhouchen Lin, Yi Ma...
We introduce the weak gap property for directed graphs whose vertex set S is a metric space of size n. We prove that, if the doubling dimension of S is a constant, any directed gra...
The increasing popularity of social networks has initiated a fertile research area in information extraction and data mining. Although such analysis can facilitate better understan...