• Corpus ID: 251564471

A measure-theoretic representation of graphs

  title={A measure-theoretic representation of graphs},
  author={Raffaella Mulas and Giulio Zucal},
Inspired by the notion of action convergence in graph limit theory, we introduce a measure–theoretic representation of matrices, and we use it to define a new notion of pseudo-metric on the space of matrices. Moreover, we show that such pseudo-metric is a metric on the subspace of adjacency or Laplacian matrices for graphs. Hence, in particular, we obtain a metric for isomorphism classes of graphs. Additionally, we study how some properties of graphs translate in this measure representation, and… 

Figures from this paper



Action convergence of operators and graphs

Abstract We present a new approach to graph limit theory that unifies and generalizes the two most well-developed directions, namely dense graph limits (even the more general $L^p$ limits) and

Subgraph densities in Markov spaces

We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set


We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field

Tracking network dynamics: A survey using graph distances

An overview of commonly-used graph distances and an explicit characterization of the structural changes that they are best able to capture, and some guidance on choosing one distance over another in different contexts are provided.

Limits of locally–globally convergent graph sequences

It is proved that even in this refined sense, the limit of a convergent graph sequence (with uniformly bounded degree) can be represented by a graphing.

Sparse Exchangeable Graphs and Their Limits via Graphon Processes

By generalizing the classical definition of graphons as functions over probability spaces to functions over $\sigma$-finite measure spaces, this work can model a large family of exchangeable graphs, including the Caron-Fox graphs and the traditional exchangeable dense graphs as special cases.

Identifiability for Graphexes and the Weak Kernel Metric

In two recent papers by Veitch and Roy and by Borgs, Chayes, Cohn, and Holden, a new class of sparse random graph processes based on the concept of graphexes over \(\sigma \)-finite measure spaces

“A and B”:

Direct fabrication of large micropatterned single crystals. p1205 21 Feb 2003. (news): Academy plucks best biophysicists from a sea of mediocrity. p994 14 Feb 2003.

The Class of Random Graphs Arising from Exchangeable Random Measures

A class of random graphs is introduced that meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks, and is given a representation theorem via a straightforward specialization of Kallenberg's representation theorem.

Large Networks and Graph Limits

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