clique tree
Recently Published Documents


TOTAL DOCUMENTS

17
(FIVE YEARS 2)

H-INDEX

5
(FIVE YEARS 0)

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 360
Author(s):  
Shaowei Sun ◽  
Kinkar Chandra Das ◽  
Yilun Shang

Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED(G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.



Author(s):  
AmirEmad Ghassami ◽  
Saber Salehkaleybar ◽  
Negar Kiyavash ◽  
Kun Zhang

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the variables. Therefore, the number of DAGs equivalent to the ground truth DAG is an indicator of the causal complexity of the underlying structure–roughly speaking, it shows how many interventions or how much additional information is further needed to recover the underlying DAG. In this paper, we propose a new technique for counting the number of DAGs in a Markov equivalence class. Our approach is based on the clique tree representation of chordal graphs. We show that in the case of bounded degree graphs, the proposed algorithm is polynomial time. We further demonstrate that this technique can be utilized for uniform sampling from a Markov equivalence class, which provides a stochastic way to enumerate DAGs in the equivalence class and may be needed for finding the best DAG or for causal inference given the equivalence class as input. We also extend our counting and sampling method to the case where prior knowledge about the underlying DAG is available, and present applications of this extension in causal experiment design and estimating the causal effect of joint interventions.



10.37236/3928 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Christoph Hofer-Temmel ◽  
Florian Lehner

We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting. 



Algorithms ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 20
Author(s):  
Anne Berry ◽  
Geneviève Simonet
Keyword(s):  


2013 ◽  
Vol 30 (3) ◽  
pp. 489-519 ◽  
Author(s):  
Anja Fischer ◽  
Frank Fischer




Sign in / Sign up

Export Citation Format

Share Document