Graph Theory What is a graph? Brief History It all began in 1736 when Leonhard Euler gave a proof that not all seven bridges over the Pregolya River could all be walked over once and end up where you started. This became known as the “Konigsberg Bridge Problem” First used to solve pu...
However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined "product measures", the products of two quantities which are zero in the extreme cases ...
Explore what is graph in data structure, its types, terminologies, representation and operations. Read on to know how to implement code in graph data structure.
As nouns the difference between graph and graphics is that graph is a diagram displaying data; in particular one showing the relationship between two or more quantities, measurements or indicative numbers that may or may not have a specific mathematical
Discrete Mathematics is a branch of mathematics that deals with how sets of numbers are arranged. It can also be used to study prime numbers, factorization, and non-repeating random sequences. There have been many uses for discrete mathematics in the modern world. Some of these uses are when...
Thus the incidence graph between real points and lines contains more structure than merely the absence of . More generally, bounding on the size of bipartite graphs (or multipartite hypergraphs) not containing a copy of some complete bipartite subgraph (or in the hypergraph case) is known as ...
This post was co-authored with Petar Veličković. See also my last year’s prediction, Michael Galkin’s excellent post on the current state of affairs in Graph ML, a deeper dive into subgraph GNNs…
There is in fact a famous theorem of Kuratowski that says that these two graphs are the only “source” of non-planarity, in the sense that any non-planar graph contains (a subdivision of) one of these graphs as a subgraph. (There is of course the even more famous four-colour theorem...
💡 This year we have really seen the rise of geometric generative models from theory to practice. A few standouts for me include Riemannian Flow Matching— in general any paper by Ricky Chen and Yaron Lipman on these topics is a must-read — and FrameDiff from Yim et...
Graph Theory is a branch of mathematics. It takes pictures as the research object. A graph in graph theory is a graph composed of a number of given...