Accurate querying of frequent subgraphs in power grid graph data

With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.

Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs

Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.

Simplifying social networks via triangle-based cohesive subgraphs

One main challenge for simplifying node-link diagrams of large-scale social networks lies in that simplified graphs generally contain dense subgroups or cohesive subgraphs.Graph triangles quantify the solid and stable relationships that maintain cohesive subgraphs.Understanding the mechanism of triangles within cohesive subgraphs contributes to illuminating patterns of connections within social networks.However,prior works can hardly handle and visualize triangles in cohesive subgraphs.In this paper,we propose a triangle-based graph simplification approach that can filter and visualize cohesive subgraphs by leveraging a triangle-connectivity called k-truss and a force-directed algorithm.We design and implement TriGraph,a web-based visual interface that provides detailed information for exploring and analyzing social networks.Quantitative comparisons with existing methods,two case studies on real-world datasets,and feedback from domain experts demonstrate the effectiveness of TriGraph.

Social Robot Detection Method with Improved Graph Neural Networks

Social robot accounts controlled by artificial intelligence or humans are active in social networks,bringing negative impacts to network security and social life.Existing social robot detection methods based on graph neural networks suffer from the problem of many social network nodes and complex relationships,which makes it difficult to accurately describe the difference between the topological relations of nodes,resulting in low detection accuracy of social robots.This paper proposes a social robot detection method with the use of an improved neural network.First,social relationship subgraphs are constructed by leveraging the user’s social network to disentangle intricate social relationships effectively.Then,a linear modulated graph attention residual network model is devised to extract the node and network topology features of the social relation subgraph,thereby generating comprehensive social relation subgraph features,and the feature-wise linear modulation module of the model can better learn the differences between the nodes.Next,user text content and behavioral gene sequences are extracted to construct social behavioral features combined with the social relationship subgraph features.Finally,social robots can be more accurately identified by combining user behavioral and relationship features.By carrying out experimental studies based on the publicly available datasets TwiBot-20 and Cresci-15,the suggested method’s detection accuracies can achieve 86.73%and 97.86%,respectively.Compared with the existing mainstream approaches,the accuracy of the proposed method is 2.2%and 1.35%higher on the two datasets.The results show that the method proposed in this paper can effectively detect social robots and maintain a healthy ecological environment of social networks.

The Game of Cops and Robbers on Directed Graphs with Forbidden Subgraphs

The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.

Forbidden Subgraphs, Distance,and Hamiltonicity

A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show that if G is.3-connected claw-free graph and(1)if for each vertex V the set of venices at distance three from v doesn’tcontain and independent subset of size three,then G is hamiltonian;(2) if G contains no induced subgraph with degree sequence(1,1,1,2,2,2,3,3,3),so that ear vertel of degree is adjacent to a vertex of degree i + 1 for i=1,2,then G is hamiltonoan. Furthermore,we obtain a generalization of both(1) and(2),in which the graphs F1 and F2coatain an the known forbidded subgraphs given in[3] as indeced subgraphs.

Extracting Semantic Subgraphs to Capture the Real Meanings of Ontology Elements

An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, which are the foundations for many applications including semantic searching, ontology matching, and linked data analysis. However, since different ontologies have different preferences to describe their elements, obtaining the semantic context of an element is an open problem. A semantic subgraph was proposed to capture the real meanings of ontology elements. To extract the semantic subgraphs, a hybrid ontology graph is used to represent the semantic relations between elements. An extracting algorithm based on an electrical circuit model is then used with new conductivity calculation rules to improve the quality of the semantic subgraphs. The evaluation results show that the semantic subgraphs properly capture the local meanings of elements. Ontology matching based on semantic subgraphs also demonstrates that the semantic subgraph is a promising technique for ontology applications.

The Hamilton-Connectivity with the Degree Sum of Non-adjacent Subgraphs of Claw-free Graphs

The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.

GRAPHS ISOMORPHIC TO SUBGRAPHS OF THEIR ITERATED LINE-GRAPHS

A graph G is said to be embedded in a graph H, written, if there exists an isomorphism φ of G onto a subgraph G’ of H. Such an isomorphism φ is called an embedding of Ginto H. In 1982, D. Bauer and R. Tindell defined an invariant for graphs G, G neither a path nor K1,3, by setting ∧（G） equal to the least n≥1 for which GL*（G）. They have studied graphs with ∧ （G）=1, and posed questions of studying graphs with ∧ （G）=2 and of determining ∧（T） for all trees T. We have also studied the questions and have further studied graphs G such that G embeds in its iterated line-graph Ln（G）.

Induced Subgraphs with Large Degrees at End-vertices for Hamiltonicity of Claw-free Graphs

A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least （[V（G）I - 2）/3. At the workshop CSzC （Novy Smokovec, 1993）, Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N （the graph obtained from a triangle by adding three disjoint pendant edges）. Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 （the graph obtained from a triangle by adding one pendant edge）. Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if eachend-vertex of every induced copy of H in G has degree at least IV（G）I/3 ＋ 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.end-vertex of every induced copy of H in G has degree at least IV（G）I/3 ＋ 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.

Discovering Cohesive Temporal Subgraphs with Temporal Density Aware Exploration

Real-world networks,such as social networks,cryptocurrency networks,and e-commerce networks,always have occurrence time of interactions between nodes.Such networks are typically modeled as temporal graphs.Mining cohesive subgraphs from temporal graphs is practical and essential in numerous data mining applications,since mining cohesive subgraphs gets insights into the time-varying nature of temporal graphs.However,existing studies on mining cohesive subgraphs,such as Densest-Exact and k-truss,are mainly tailored for static graphs(whose edges have no temporal information).Therefore,those cohesive subgraph models cannot indicate both the temporal and the structural characteristics of subgraphs.To this end,we explore the model of cohesive temporal subgraphs by incorporating both the evolving and the structural characteristics of temporal subgraphs.Unfortunately,the volume of time intervals in a temporal network is quadratic.As a result,the time complexity of mining temporal cohesive subgraphs is high.To efficiently address the problem,we first mine the temporal density distribution of temporal graphs.Guided by the distribution,we can safely prune many unqualified time intervals with the linear time cost.Then,the remaining time intervals where cohesive temporal subgraphs fall in are examined using the greedy search.The results of the experiments on nine real-world temporal graphs indicate that our model outperforms state-of-the-art solutions in efficiency and quality.Specifically,our model only takes less than two minutes on a million-vertex DBLP and has the highest overall average ranking in EDB and TC metrics.

Discriminative subgraphs for discovering family photos

We propose to use discriminative subgraphs to discover family photos from group photos in an efficient and effective way. Group photos are represented as face graphs by identifying social contexts such as age, gender, and face position. The previous work utilized bag-of-word models and considered frequent subgraphs from all group photos as features for classification. This approach, however, produces numerous subgraphs, resulting in high dimensions.Furthermore, some of them are not discriminative.To solve these issues, we adopt a state-of-the-art,frequent subgraph mining method that removes nondiscriminative subgraphs. We also use TF-IDF normalization, which is more suitable for the bag-ofword model. To validate our method, we experiment in two datasets. Our method shows consistently better performance, higher accuracy in lower feature dimensions, compared to the previous method. We also integrate our method with the recent Microsoft face recognition API and release it in a public website.

Self-similarity of complex networks under centrality-based node removal strategy

Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality reduction techniques that can significantly reduce the structural complexity of initial large-scale networks.In this paper,we propose a subgraph extraction method based on the node centrality measure to reduce the size of the initial network topology.Specifically,nodes with smaller centrality value are removed from the initial network to obtain a subgraph with a smaller size.Our results demonstrate that various real-world networks,including power grids,technology,transportation,biology,social,and language networks,exhibit self-similarity behavior during the reduction process.The present results reveal the selfsimilarity and scale invariance of real-world networks from a different perspective and also provide an effective guide for simplifying the topology of large-scale networks.

Exact Graph Pattern Matching:Applications,Progress and Prospects

Graph pattern matching(GPM)can be used to mine the key information in graphs.Exact GPM is one of the most commonly used methods among all the GPM-related methods,which aims to exactly find all subgraphs for a given query graph in a data graph.The exact GPM has been widely used in biological data analyses,social network analyses and other fields.In this paper,the applications of the exact GPM were first introduced,and the research progress of the exact GPM was summarized.Then,the related algorithms were introduced in detail,and the experiments on the state-of-the-art exact GPM algorithms were conducted to compare their performance.Based on the experimental results,the applicable scenarios of the algorithms were pointed out.New research opportunities in this area were proposed.

An Evolutionary Algorithm Coupled to an Outranking Method for the Multicriteria Shortest Paths Problem

In this article, we are interested in solving a combinatorial optimization problem, the shortest path problem in a multi-attribute graph, by the out-ranking methods. A multi-attribute graph has simultaneously qualitative and quantitative criteria. This situation gives rise to incomparable paths thus forming the Pareto front. Outranking methods in Multi-criteria Decision Making (MCDM) are the only methods that can take into account this situation (incomparability of actions). After presenting the categories of Multi-criteria Decision Making (MCDM) and the difficulties related to the problems of the shortest paths, we propose an evolutionary algorithm based on the outranking methods to solve the problem of finding “best” paths in a multi-attribute graph with non-additive criteria. Our approach is based on the exploration of induced subgraphs of the outranking graph. Properties have been established to serve as algorithmic basis. Numerical experiments have been carried out and the results presented in this article.

Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties

The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the operation induces addition or subtraction on the pairs of ai, aj elements which are consecutive pairs of elements obtained from a generating set of some finite order. The paper identifies that the set of the generated pairs of integer sequence is non-associative. The paper also presents the graph theoretic applications of the integers generated in which subgraphs are deduced from the main graph and adjacency matrices and incidence matrices constructed. It was also established that some of the subgraphs were found to be regular graphs. The findings in this paper can further be used in coding theory, Boolean algebra and circuit designs.

Data-driven Product Functional Confguration:Patent Data and Hypergraph

The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize functional confgurations using patent data.This study frst proposes a patent-data-driven PFC method based on a hypergraph network.It then constructs a weighted network model to optimize the combination of product function quantity and object from the perspective of big data,as follows:(1)The functional knowledge contained in the patent is extracted.(2)The functional hypergraph is constructed based on the co-occurrence relationship between patents and applicants.(3)The function and patent weight are calculated from the patent applicant’s perspective and patent value.(4)A weight calculation model of the PFC is developed.(5)The weighted frequent subgraph algorithm is used to obtain the optimal function combination list.This method is applied to an innovative design process of a bathroom shower.The results indicate that this method can help frms detach optimal function candidates and develop a multifunctional product.

Design Pattern Mining Using Graph Matching

The identification of design pattern instances is important for program understanding and software maintenance. Aiming at the mining of design patterns in existing systems, this paper proposes a subgraph isomorphism approach to discover several design patterns in a legacy system at a time. The attributed relational graph is used to describe design patterns and legacy systems. The sub-graph isomorphism approach consists of decomposition and composition process. During the decomposition process, graphs corresponding to the design patterns are decomposed into sub-graphs, some of which are graphs corresponding to the elemental design patterns. The composition process tries to get sub-graph isomorphism of the matched graph if sub-graph isomorphism of each subgraph is obtained. Due to the common structures between design patterns, the proposed approach can reduce the matching times of entities and relations. Compared with the existing methods, the proposed algorithm is not linearly dependent on the number of design pattern graphs. Key words design pattern mining - attributed relational graph - subgraph isomorphism CLC number TP 311.5 Foundation item: Supported by the National Natural Science Foundation of China (60273075) and the Science Foundation of Naval University of Engineering (HGDJJ03019)Biography: LI Qing-hua (1940-), male, Professor, research direction: parallel computing.

A Clique-Based Approach to the Identification of Common Gene Association Sub-Networks

We developed a computational framework to identify common gene association sub-network. This framework combines graphical lasso model, graph product and a replicator equation based clique solver. We applied this method to find common stress responsive sub-networks from two related Deinococcus-Thermus bacterial species.

Subgraph Matching Using Graph Neural Network

Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.