• Corpus ID: 14506802

Large Networks and Graph Limits

  title={Large Networks and Graph Limits},
  author={Martin B{\'a}lek and Andrew J. Goodall}
The book Large Networks and Graph Limits, xiv + 475 pp., published in late 2012, comprises five parts, the first an illuminating introduction and the last a tantalizing taste of how the scope of the theory developed in its pages might be extended to other combinatorial structures than graphs. The three central parts treat in depth the topics of graph algebras, limits for sequences of dense graphs (this constitutes the most substantial part, occupying nearly half the book) and limits for… 
Ordered Graph Limits and Their Applications
An ordered analogue of the well-known result by Alon and Stav on the furthest graph from a hereditary property is proved, the first known result of this type in the ordered setting, and an alternative analytic proof of the ordered graph removal lemma is described.
Random Geometric Graph: Some recent developments and perspectives
This paper surveys the recent developments in RGGs from the lens of high dimensional settings and non-parametric inference and explains how this model differs from classical community based random graph models.
Maximum spread of graphs and bipartite graphs
Given any graph G, the (adjacency) spread of G is the maximum absolute difference between any two eigenvalues of the adjacency matrix of G. In this paper, we resolve a pair of 20-year-old conjectures
An introduction to large deviations for random graphs
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the
A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth
A general framework for the study of limits of relational structures in general and graphs in particular is introduced, which is based on a combination of model theory and (functional) analysis and that the various approaches to graph limits fit to this framework and that they naturally appear as "tractable cases" of a general theory.
Random homomorphisms into the orthogonality graph
Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequences). While limit
Spectral Theory of Graphons
Many new fields in graph theory have develop in the last half century involve and incorporate other branches of mathematics. Utilizing linear algebra, spectral graph theory has been an ever-growing
Estimating the Number of Connected Components in a Graph via Subgraph Sampling
It is shown that it is impossible if the parent graph is allowed to contain high-degree vertices or long induced cycles and characterized the optimal sample complexity within constant factors and construct linear-time estimators that provably achieve these bounds.
Queues, random graphs, and queues on random graphs
The work presented in this thesis lies on the interface of two key areas in probability theory, namely queueing theory and random graph theory, which introduces and analyzes two models of randomly evolving graphs.
The topology of solution spaces of combinatorial problems
Graph homomorphism is a notion almost as simple, notationally and conceptually, as graph coloring, but one that gives a rich mathematical structure, allowing for new fruitful connections with algebra