DeepAI AI Chat
Log In Sign Up

The Metric Space of Networks

04/09/2018
by   Samir Chowdhury, et al.
The Ohio State University
0

We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak isomorphism. Then we identify a definition of distance on the space of all networks that is compatible with weak isomorphism. This global approach comes equipped with notions such as completeness, compactness, curves, and geodesics, which we explore throughout this paper. Furthermore, it admits global-to-local inference in the following sense: we prove that two networks are weakly isomorphic if and only if all their motif sets are identical, thus answering the network reconstruction question. Further exploiting the additional structure imposed by our network distance, we prove that two networks are weakly isomorphic if and only if certain essential associated structures---the skeleta of the respective networks---are strongly isomorphic.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/06/2020

Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups

We study the periodicity of subshifts of finite type (SFT) on Baumslag-S...
11/21/2021

Strictification of weakly stable type-theoretic structures using generic contexts

We present a new strictification method for type-theoretic structures th...
06/21/2021

Recolouring weakly chordal graphs and the complement of triangle-free graphs

For a graph G, the k-recolouring graph ℛ_k(G) is the graph whose vertice...
02/17/2020

On the Approximability of Weighted Model Integration on DNF Structures

Weighted model counting admits an FPRAS on DNF structures. We study weig...
06/27/2022

Definable and Non-definable Notions of Structure

Definability is a key notion in the theory of Grothendieck fibrations th...
12/16/2022

Weakly weighted generalised quasi-metric spaces and semilattices

Motivated by recent applications to entropy theory in dynamical systems,...
11/18/2022

On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces

We show that the locally strongly sober spaces are exactly the coherent ...