Search Results (13)

Practical algorithms for computing canonical forms of multi-digraphs do not exist in the literature. This paper proposes two practical approaches for finding canonical forms, from the perspective of nD symbolic computation. Initially, the approaches turn the problem of finding canonical forms of multi-digraphs into computing canonical forms of indexed monomials in computer algebra. Then, the first approach utilizes the double coset representative method in computational group theory for canonicalization of indexed monomials and shows that finding the canonical forms of a class of multi-digraphs in practice has polynomial complexity of approximately $O\left({(k+p)}^2\right)$ or $O\left(k^{2.1}\right)$ by the computer algebra system (CAS) tool Tensor-canonicalizer. The second approach verifies the equivalence of canonicalization of indexed monomials and finding canonical forms of (simple) colored tripartite graphs. It is found that the proposed algorithm takes approximately $O\left({(k+2p)}^{4.803}\right)$ time for a class of multi-digraphs in practical implementation, combined with one of the best known graph isomorphism tools Traces, where k and p are the vertex number and edge number of a multi-digraph, respectively. Full article

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems. Full article

Intelligent medical systems have great potential to play an important role in people’s daily lives, as they can provide disease and medicine information immediately for both doctors and patients. Graph-structured data are attracting more and more attention in the artificial intelligence sector. Combining graph-structured data with a medical data set, a tripartite graph convolutional network named TriGCN is proposed. This model is able connect to disease and medicine or patient, disease, and medicine nodes, propagate information from layer to layer, and update node features at the same time. After this, calibrated label ranking is used to give personalized medicine recommendation lists to patients. The TriGCN approach has a great performance, outperforming other machine learning methods. Thus, this model has the potential to be applied in reality and will provide contributions to public health in the future. Full article

A connected graph, G, is Crossing Free-connected ($\mathcal{CF}$-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete tripartite graph, $K_{l,m,n}$, is $\mathcal{CF}$-connected if and only if it does not contain any of the following as a subgraph: $K_{1,2,7}$, $K_{1,3,5}$, $K_{1,4,4}$, $K_{2,2,5}$, $K_{3,3,3}$. We examine the idea that $K_{1,2,7}$, $K_{1,3,5}$, $K_{1,4,4}$, and $K_{2,2,5}$ are the first non-$\mathcal{CF}$-connected complete tripartite graphs. The $\mathcal{CF}$-connectedness of $K_{l,m,n}$ with $l,m,n\ge 3$ is dependent on the knowledge of crossing numbers of $K_{3,3,n}$. In this paper, we prove various results that support this conjecture. Full article

Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory. This paper aims to determine the crossing number of the join product $G^{*}+D_n$, where $G^{*}$ is a connected graph isomorphic to $K_{2,2,2}\setminus \{e_1,e_2\}$ obtained by removing two edges $e_1,e_2$ with a common vertex and a second vertex from the different partitions of the complete tripartite graph $K_{2,2,2}$, and $D_n$ is a discrete graph composed of n isolated vertices. The proofs utilize known exact crossing number values for join products of specific subgraphs $H_k$ of $G^{*}$ with discrete graphs in combination with the separating cycles. Similar approaches can potentially estimate unknown crossing numbers of other six-vertex graphs with a larger number of edges in join products with discrete graphs, paths or cycles. Full article

Identifying drug–target interactions is a crucial step in discovering novel drugs and for drug repositioning. Network-based methods have shown great potential thanks to the straightforward integration of information from different sources and the possibility of extracting novel information from the graph topology. However, despite recent advances, there is still an urgent need for efficient and robust prediction methods. Here, we present SimSpread, a novel method that combines network-based inference with chemical similarity. This method employs a tripartite drug–drug–target network constructed from protein–ligand interaction annotations and drug–drug chemical similarity on which a resource-spreading algorithm predicts potential biological targets for both known or failed drugs and novel compounds. We describe small molecules as vectors of similarity indices to other compounds, thereby providing a flexible means to explore diverse molecular representations. We show that our proposed method achieves high prediction performance through multiple cross-validation and time-split validation procedures over a series of datasets. In addition, we demonstrate that our method performed a balanced exploration of both chemical ligand space (scaffold hopping) and biological target space (target hopping). Our results suggest robust and balanced performance, and our method may be useful for predicting drug targets, virtual screening, and drug repositioning. Full article

For a graph $G=(V,E)$ and a set $S\subseteq V\left(G\right)$ of a size at least 2, a path in G is said to be an S-path if it connects all vertices of S. Two S-paths $P_1$ and $P_2$ are said to be internally disjoint if $E\left(P_1\right)\cap E\left(P_2\right)=\varnothing$ and $V\left(P_1\right)\cap V\left(P_2\right)=S$; that is, they share no vertices and edges apart from S. Let ${\pi }_G\left(S\right)$ denote the maximum number of internally disjoint S-paths in G. The k-path-connectivity ${\pi }_k\left(G\right)$ of G is then defined as the minimum ${\pi }_G\left(S\right)$, where S ranges over all k-subsets of $V\left(G\right)$. In this paper, we study the k-path-connectivity of the complete balanced tripartite graph $K_{n,n,n}$ and obtain ${\pi }_k\left(K_{n,n,n}\right)=⌊\frac{2n}{k-1}⌋$ for $3\le k\le n.$ Full article

We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems. Full article

The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph $K_{1,1,3}\backslash e$ obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph $K_{1,1,3}$. The proofs are done with the help of well-known exact values for the crossing numbers of the join products of subgraphs of the considered graph with paths and cycles. Finally, by adding some edges to the graph under consideration, we obtain the crossing numbers of the join products of other graphs with the paths and the cycles on n vertices. Full article

With the increasing reliance on global sourcing and the growth in the likelihood of disruptive incidents, today’s supply networks are more prone to unexpected natural and man-made disruptive events. In order to alleviate the losses caused by these disruptive events, when a large-scale event disrupts multiple suppliers simultaneously, a single or several critical suppliers should be selected from the disrupted ones to assist them to recover their production as soon as possible. The selection of these recovery suppliers is of great importance in the recovery process of the entire supply network. Thus, this paper proposes a recovery supplier selection method from the view of the supply network structure. Firstly, a tripartite graph-based supply model is proposed to depict a two-stage supply network, which consists of multiple manufacturers and suppliers as well as the diverse product supply-demand interdependence connecting them. To measure the impacts caused by supplier disruptions and to evaluate the effectiveness of recovery supplier decisions, two supply network performance metrics reflecting product supply availability are also given. Then, the recovery supplier selection problem is described as a combinatorial optimization problem. To solve this problem, a heuristic algorithm, with enhanced variable neighborhood search (EVNS) is designed based on the general framework of a variable neighborhood search. Finally, experiments based on a real-world supply network are conducted. The experimental results indicate that the proposed method is applicable and effective. Full article

Cross-domain relation extraction has become an essential approach when target domain lacking labeled data. Most existing works adapted relation extraction models from the source domain to target domain through aligning sequential features, but failed to transfer non-local and non-sequential features such as word co-occurrence which are also critical for cross-domain relation extraction. To address this issue, in this paper, we propose a novel tripartite graph architecture to adapt non-local features when there is no labeled data in the target domain. The graph uses domain words as nodes to model the co-occurrence relation between domain-specific words and domain-independent words. Through graph convolutions on the tripartite graph, the information of domain-specific words is propagated so that the word representation can be fine-tuned to align domain-specific features. In addition, unlike the traditional graph structure, the weights of edges innovatively combine fixed weight and dynamic weight, to capture the global non-local features and avoid introducing noise to word representation. Experiments on three domains of ACE2005 datasets show that our method outperforms the state-of-the-art models by a big margin. Full article

Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system. Full article

Points of interest (POIs) such as stores, gas stations, and parking lots are particularly important for maps. Using gas station as a case study, this paper proposed a novel approach to enhance POI information using low-frequency vehicle trajectory data and social media data. First, the proposed method extracted spatial information of the gas station from sparse vehicle trace data in two steps. The first step proposed the velocity sequence linear clustering algorithm to extract refueling stop tracks from the individual trace line after modeling the vehicle refueling stop behavior using movement features. The second step used the Delaunay triangulation to extract the spatial information of gas stations from the collective refueling stop tracks. Second, attribute information and dimension sentiment semantic information of the gas station were extracted from social media data using the text mining method and tripartite graph model. Third, the gas station information was enhanced by fusing the extracted spatial data and semantic data using a matching method. Experiments were conducted using the 15-day vehicle trajectories of 12,000 taxis and social media data from the Dazhongdianping in Beijing, China, and the results showed that the proposed method could extract the spatial information, attribute information, and review information of gas stations simultaneously. Compared with ground truth data, the automatically enhanced gas station was proved to be of higher quality in terms of the correctness, completeness, and real-time. Full article