A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

A graph is a good way to illustrate some relations between things. But, not all relations can be illustrated by this graph. So, in this paper we will define a new type of graph, we call it a ...

This is a preview. Log in through your library . Abstract This paper is mainly concerned with the realizability of a set of n integers as the degrees of vertices of an n-vertex linear graph. Other ...

This repository contains Java implementations of two fundamental graph algorithms: Kruskal's algorithm for finding the minimum spanning tree (MST) and Dijkstra's algorithm for finding the shortest ...

Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the development of ...

Spectral graph clustering—clustering the vertices of a graph based on their spectral embedding—is of significant current interest, finding applications throughout the sciences. But as with clustering ...