Let G be a directed graph such that every edge e of G is associated with a positive integer, called the index of e. Then G is called a network graph if, at every vertex v of G, the sum of the indices ...

Well, if I remember my graph theory well enough, if A is the adjacency matrix of the graph, each entry of A^n is the number of ways to get between the corresponding nodes in n steps or less. So, to do ...

Deep in the heart of Microsoft, Jennifer Chayes and Christian Borgs lead a who's who of mathematics and computer science. The goal? To explore anything they please Every weekday afternoon some 20 ...

This is a preview. Log in through your library . Abstract In this paper, we establish the existence of common fixed points of multivalued F-contraction mappings on a metric space endowed with a graph.

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

When you get stuck on a fiendishly difficult sudoku, it’s hard not to wonder if the puzzle really has a solution. At another moment, aglow in the triumph of a clever deduction, you might have a ...

Understanding the network organization of the brain has been a long-standing challenge for neuroscience. In the past decade, developments in graph theory have provided many new methods for ...