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Discrete Graphical Models and Their Parameterization
Published in Marloes Maathuis, Mathias Drton, Steffen Lauritzen, Martin Wainwright, Handbook of Graphical Models, 2018
Luca La Rocca, Alberto Roverato
An example of mixed graph is given in Figure 8.2(iii). Models defined by mixed graphs with only undirected edges are UG models, whereas models defined by mixed graphs with only directed edges are DAG models. Furthermore, models defined by mixed graphs with only bidirected edges form the family of BG models. This is a class of models of marginal independence introduced by Kauermann [31]. Independencies can be read off a bidirected graph through the dual global Markov property, which means for instance that Xfh $ X_{ fh} $ and Xe $ X_{e} $ are independent in the model defined by the graph in Figure 8.2(ii). This should be compared with Xbd $ X_{bd} $ and Xc $ X_{c} $ being conditionally independent given Xa $ X_{a} $ in the UG model for the graph of Figure 8.2(i).
Shortest Path Models and Algorithms
Published in Craig A. Tovey, Linear Optimization and Duality, 2020
In a weighted mixed graph, every edge has a weight. However, some edges are directed and the other edges are undirected. Prove that finding a minimum weight simple path in a mixed graph is NP-hard, as is the detection of negative weight cycles [8].
Graph based CNN Algorithm to Detect Spammer Activity Over Social Media
Published in IETE Journal of Research, 2022
Aditya Tandon, Shouvik Kumar Guha, Junaid Rashid, Jungeun Kim, Mamta Gahlan, Mohammad Shabaz, Nasreen Anjum
This method obtains a node's feature representation vector by utilizing the information included in the network structure's random walk sequence. The homogeneity of the network's local structure is the only factor considered by this method. Node2vec [18]: It is possible to significantly improve the DeepWalk algorithm by altering the approach used for the production of random walk sequences. DeepWalk selects the next node in the random walk sequence using uniform random distribution to ensure that the series continues. At the same time, Node2vec introduces two parameters, p and q, which are used in the process of producing random walk sequences. Breadth-first search and depth-first search are both used in the process of generating random walk sequences. The homogeneity and isomorphism of the network's local structure are the only considerations for this strategy.Struc2vec [12]: By strictly defining the structural isomorphism of nodes, Struc2vec uses the M-layer structure homogeneity graph to reconstruct the multilayer mixed graph of node similarity and then uses a random walk and language model to obtain the characteristics of the node Vector representation. This method only considers the isomorphism of the global structure of the network.
A bi-objective transportation-location arc routing problem
Published in Transportation Letters, 2020
Alireza Amini, Reza Tavakkoli-Moghaddam, Sadoullah Ebrahimnejad
The LARP’s graphs can be undirected, directed, or mixed (Albareda-Sambola 2015). This study takes a mixed graph into account. According to the respective literature, the LARP belongs to NP-hard problems. So, the TLARP will also become NP-hard. So, two meta-heuristics are employed: NSGA-II and also its combination with multi-objective late acceptance hill-climbing (MOLAHC) algorithm. Local search algorithms will also be implemented to enhance the performance level of the algorithms.
Algorithmic graph theory for post-processing molecular dynamics trajectories
Published in Molecular Physics, 2023
Sana Bougueroua, Ylène Aboulfath, Dominique Barth, Marie-Pierre Gaigeot
A molecular conformation is defined by a mixed graph, denoted 2D-MolGraph, where V is the set of all atoms of the molecular system except hydrogen atoms that are not accounted for. Each atom of the molecular system is a vertex of G. The sets and are respectively the covalent bonds, hydrogen bonds, electrostatic interactions, and organometallic interactions that can be encountered between the atoms of the molecular system. They are the edges and arcs (directed edges) of the graph G. We note E the undirected edges of the graph and A the directed edges (arcs). The model has been designed so that it can be extended to any type of bond between two atoms and to any kind of interaction between atoms. We hence started our developments of 2D-topological graphs for gas phase molecules in which only covalent bonds and hydrogen bonds were considered relevant for the description of the conformation over time (e.g. for peptides). The 2D-graphs were then extended to molecular systems in which ions (anions, cations) are present and hence interact with atoms through 'electrostatic interactions' denoted in the 2D-MolGraphs. Such interactions were then included in the conformational analysis and our topological 2D-MolGraphs. We recently applied our 2D-graphs and graph algorithms to molecular clusters of interest in homogeneous catalysis [46]. In these molecular systems, metallic atoms such as, e.g. Manganese, Ruthenium or Gold, interact with the other atoms of the cluster. We hence defined 'organometallic interactions' to take these interactions into account into the 2D-MolGraphs. To keep the information related to the hydrogen atom involved in H-bonds, directed edges (arcs) are hence used with the convention that the edge is directed from the heavy atom to the donor. There is therefore no need to include explicitly the hydrogen atoms in the 2D-MolGraphs, only the ones involved in H-bonds are incorporated through the directed edges. More details are found in ref. [42].