Permanental Graphs

09/23/2020
by   Daniel Xiang, et al.
0

The two components for infinite exchangeability of a sequence of distributions (P_n) are (i) consistency, and (ii) finite exchangeability for each n. A consequence of the Aldous-Hoover theorem is that any node-exchangeable, subselection-consistent sequence of distributions that describes a randomly evolving network yields a sequence of random graphs whose expected number of edges grows quadratically in the number of nodes. In this note, another notion of consistency is considered, namely, delete-and-repair consistency; it is motivated by the sense in which infinitely exchangeable permutations defined by the Chinese restaurant process (CRP) are consistent. A goal is to exploit delete-and-repair consistency to obtain a nontrivial sequence of distributions on graphs (P_n) that is sparse, exchangeable, and consistent with respect to delete-and-repair, a well known example being the Ewens permutations <cit.>. A generalization of the CRP(α) as a distribution on a directed graph using the α-weighted permanent is presented along with the corresponding normalization constant and degree distribution; it is dubbed the Permanental Graph Model (PGM). A negative result is obtained: no setting of parameters in the PGM allows for a consistent sequence (P_n) in the sense of either subselection or delete-and-repair.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/22/2016

Edge-exchangeable graphs and sparsity

A known failing of many popular random graph models is that the Aldous-H...
research
08/02/2021

Node repair on connected graphs

We study the problem of erasure correction (node repair) for regeneratin...
research
07/18/2023

Rule-based Graph Repair using Minimally Restricted Consistency-Improving Transformations

Model-driven software engineering is a suitable method for dealing with ...
research
08/10/2011

A consistent adjacency spectral embedding for stochastic blockmodel graphs

We present a method to estimate block membership of nodes in a random gr...
research
03/21/2020

Weighted directed networks with a differentially private bi-degree sequence

The p_0 model is an exponential random graph model for directed networks...
research
05/08/2020

Graph Consistency as a Graduated Property: Consistency-Sustaining and -Improving Graph Transformations

Where graphs are used for modelling and specifying systems, consistency ...
research
08/20/2020

Variance and covariance of distributions on graphs

We develop a theory to measure the variance and covariance of probabilit...

Please sign up or login with your details

Forgot password? Click here to reset