Set Of Subgraphs Research Articles

TipTap: Approximate Mining of Frequent k -Subgraph Patterns in Evolving Graphs

“Perhaps he could dance first and think afterwards, if it isn’t too much to ask him.” S. Beckett, Waiting for Godot Given a labeled graph, the collection of k -vertex induced connected subgraph patterns that appear in the graph more frequently than a user-specified minimum threshold provides a compact summary of the characteristics of the graph, and finds applications ranging from biology to network science. However, finding these patterns is challenging, even more so for dynamic graphs that evolve over time, due to the streaming nature of the input and the exponential time complexity of the problem. We study this task in both incremental and fully-dynamic streaming settings, where arbitrary edges can be added or removed from the graph. We present TipTap , a suite of algorithms to compute high-quality approximations of the frequent k -vertex subgraphs w.r.t. a given threshold, at any time (i.e., point of the stream), with high probability. In contrast to existing state-of-the-art solutions that require iterating over the entire set of subgraphs in the vicinity of the updated edge, TipTap operates by efficiently maintaining a uniform sample of connected k -vertex subgraphs, thanks to an optimized neighborhood-exploration procedure. We provide a theoretical analysis of the proposed algorithms in terms of their unbiasedness and of the sample size needed to obtain a desired approximation quality. Our analysis relies on sample-complexity bounds that use Vapnik–Chervonenkis dimension, a key concept from statistical learning theory, which allows us to derive a sufficient sample size that is independent from the size of the graph. The results of our empirical evaluation demonstrates that TipTap returns high-quality results more efficiently and accurately than existing baselines.

Colored Network Motif Analysis by Dynamic Programming Approach: An Application in Host Pathogen Interaction Network

Network motifs are subgraphs of a network which are found with significantly higher frequency than that expected in similar random networks. Motifs are small building blocks of a network and they have emerged as a way to uncover topological properties of complex networks. A special yet not much explored type of motif is the 'colored motif' where color (type) of each node, and hence the edges, in the motif is distinguishable from each other. A traditional motif is defined as a recurring structure in a network, whereas colored motif introduces detailed information about the color of the nodes. G-trie is a data structure to efficiently store a given set of subgraphs by exploiting the topological overlaps within them. In this article we have implemented a modified g-trie to store colored subgraphs and developed a method to discover colored motifs. Our method uses an approximate enumeration for counting the subgraphs to reduce the runtime. We have applied our method to find colored motifs of size three in a host pathogen protein-protein interaction network having two types of proteins namely HIV-1 and human proteins, and four types of edges. Here, we have discovered eight motifs, six of which contain both HIV-1 and human proteins, while the remaining two contain only human proteins.

Graph partitioning and graph neural network based hierarchical graph matching for graph similarity computation

Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action Recognition. Recently, some graph similarity computation models based on neural networks have been proposed, which are either based on graph-level interaction or node-level comparison. However, when the number of nodes in the graph increases, it will inevitably bring about reduced representation ability or high computation cost.Motivated by this observation, we propose a graph partitioning and graph neural network-based model, called PSimGNN, to effectively resolve this issue. Specifically, each of the input graphs is partitioned into a set of subgraphs to extract the local structural features directly. Next, a novel graph neural network with an attention mechanism is designed to map each subgraph into an embedding vector. Some of these subgraph pairs are automatically selected for node-level comparison to supplement the subgraph-level embedding with fine-grained information. Finally, coarse-grained interaction information among subgraphs and fine-grained comparison information among nodes in different subgraphs are integrated to predict the final similarity score. Experimental results on graph datasets with different graph sizes demonstrate that PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks using approximate Graph Edit Distance (GED) as the graph similarity metric.

Super Ck and Sub-Ck Connectivity of k-Ary n-Cube Networks

Let [Formula: see text] be an undirected graph. An [Formula: see text]-structure-cut (resp. [Formula: see text]-substructure-cut) of [Formula: see text] is a set of subgraphs of [Formula: see text], if any, whose deletion disconnects [Formula: see text], where the subgraphs deleted are isomorphic to a certain graph [Formula: see text] (resp. where for any [Formula: see text] of the subgraphs deleted, there is a subgraph [Formula: see text] of [Formula: see text], isomorphic to [Formula: see text], such that [Formula: see text] is a subgraph of [Formula: see text]). [Formula: see text] is super[Formula: see text]-connected (resp. super sub-[Formula: see text]-connected) if the deletion of an arbitrary minimum [Formula: see text]-structure-cut (resp. minimum [Formula: see text]-substructure-cut) isolates a component isomorphic to a certain graph [Formula: see text]. The [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] is one of the most attractive interconnection networks for multiprocessor systems. In this paper, we prove that [Formula: see text] with [Formula: see text] is super sub-[Formula: see text]-connected if [Formula: see text] and [Formula: see text] is odd, and super [Formula: see text]-connected if [Formula: see text] and [Formula: see text] is odd.

Efficient (k, α)-Maximal-Cliques Enumeration Over Uncertain Graphs

A maximal clique ( ${MC}$ ) is a complete subgraph satisfying that no other cliques can take it as their proper subgraph. Given an uncertain graph, the $top\text{-}K\,\,{MC}\text{s}$ enumeration problem studies how to return $k {MC}\text{s}$ with the highest rank value. Existing algorithms rank ${MC}\text{s}$ according to their probabilities, thus usually return ${MC}\text{s}$ with higher probabilities but less number of vertices, and fail to return large ${MC}\text{s}$ that convey more useful information. Considering this problem, this paper studies the problem of enumerating $top\text{-}K\,\,{MC}\text{s}$ . Our approach returns $k {MC}\text{s}$ with the most number of vertices satisfying that their probabilities $\geq \alpha $ , where each ${MC}$ is called an $\alpha $ - ${MC}$ , and computing $k$ largest $\alpha $ - ${MC}\text{s}$ is called as $(k,\alpha)$ - ${MC}\text{s}$ . We propose an efficient $(k,\alpha)$ - ${MC}\text{s}$ enumeration algorithm, $Top\text{-}KMC$ , which works in three steps, including partition, enumeration and verification. Here, partition means that we compute the set $\mathcal {M}$ of all ${MC}\text{s}$ without considering the probability information, as if the graph is partitioned into a set of subgraphs. Enumeration means that we compute $\alpha $ - ${MC}\text{s}$ from each ${MC}$ of $\mathcal {M}$ . As each such subgraph is an ${MC}$ , the cost of computing common neighbors for finding $\alpha $ - ${MC}\text{s}$ can be reduced. Verification means that we need to verify whether an $\alpha $ - ${MC}$ is a subgraph of another $\alpha $ - ${MC}$ . If not, it is an $\alpha $ - ${MC}$ ; otherwise, it is a useless $\alpha $ - ${MC}$ and should be removed. We further propose an optimized algorithm $Top\text{-}KMC+$ to reduce both time and space by merging the above three steps into a whole step. The experimental results on real datasets show that both $Top\text{-}KMC$ and $Top\text{-}KMC+$ can return $k$ largest $\alpha $ - ${MC}\text{s}$ efficiently.

SARO: Scalable Attack-Resistant Logic Locking

Intellectual property (IP) protection against piracy and reverse engineering (RE) has emerged as a critical area of research in the field of hardware security. Logic locking has been studied as a promising technique to provide robust protection against these attacks. However, a vast body of recent works has presented successful attacks to break existing locking methods in terms of retrieving the secret key and restoring the original functionality. In this paper, we propose SARO, a scalable attack-resistant logic locking that provides a robust functional and structural design transformation process. SARO treats the target circuit as a hypergraph (G), and performs partitioning of G to produce a set of sub-graphs, then applies an efficient Truth Table Transformation (T3) process to each partition. Further, to mitigate specific attacks (such as SAT-based analysis), SARO implements distributed attack resistance, which integrates random SAT-hard functions (obtained from an automatic function generator, RanSAT) into select partitions. RanSAT produces non-biased and non-deterministic design transformations, where added locking mechanisms are not distinguishable from the original circuit. Finally, it implements a concept of a derived key generation that simultaneously helps to minimize the required key size through judicious reuse of key bits, as well as enhancing the structural alterations. Unlike state-of-the-art logic locking solutions, which focus on primarily enhancing robustness against functional query-based attacks, the proposed transformation steps provide the following unique benefits: (1) high scalability to large designs obtained through partitioning; (2) high structural obfuscation leading to resistance to structural attacks; and (3) low key size, while maintaining strong resistance against functional attacks. To quantitatively represent the level of structural and functional transformation, we also propose the T3 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">metric</sub> . We evaluate SARO on ISCAS85 and EPFL benchmarks, and provide comprehensive security and performance analysis of our proposed framework.

Corpus-Based Syntactic-Semantic Graph Analysis

This research exemplifies the corpus-based graph approach to the syntactic-semantic analysis of a concept feeling using the Construction Grammar Conceptual network methodology. by constructing a lexical network from grammatically tagged collocations of the english and the Croatian web corpora, the structure of the semantic domains is revealed as a set of sub-graphs derived from the source lexeme’s friend-of-a-friend graph. the subgraph structures, calculated with the community detection algorithm, are interpreted as the semantic domains associated with the source lexeme’s conceptual matrix. lexical structures are analyzed using a centrality algorithm that determines the overall rank of the salience and semantic relatedness to the source concept feeling. this empirical approach can be used for developing nlP methods and tasks, such as computing semantic similarity, sense disambiguation, sense structuring, as well as for comparative corpus and cross-cultural studies. ConGraCnet has a web application on the page &lt;a target="_blank" rel="nofollow" href="http://emocnet.uniri.hr/congracnet"&gt;http://emocnet.uniri.hr/congracnet&lt;/a&gt;.

Structure connectivity and substructure connectivity of wheel networks

Consider a graph G and its connected subgraph T. The T-structure connectivity κ(G;T) of G is the cardinality of a minimum set of subgraphs in G, whose removal disconnects G and each element in the set is isomorphic to T. The T-substructure connectivity κs(G;T) of G is the cardinality of a minimum set of subgraphs in G, whose removal disconnects G and each element in the set is isomorphic to a connected subgraph of T. In G, the standard connectivity κ(G) is regarded as a simplification of both κ(G;T) and κs(G;T). The wheel network, denoted by CWn, is an attractive interconnected network prototype for multiple CPU systems. In this paper, we determine κ(CWn;P2k+1) (resp. κs(CWn;P2k+1)) for n≥5 and k+1≤2n−4, κ(CWn;P2k) (resp. κs(CWn;P2k)) for n≥6 and k≤2n−4 and a lower bound of κ(CWn;C2k) (resp. κs(CWn;C2k)) for n≥6 and k≤2n−4.

On the crossing number of join product of the discrete graph with special graphs of order five

The main aim of the paper is to give the crossing number of join product G + D n for the disconnected graph G of order five consisting of the complete graph K 4 and of one isolated vertex. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G onto the set of subgraphs which cross the edges of the graph G exactly one times. All methods used in the paper are new, and they are based on combinatorial properties of cyclic permutations. Finally, by adding some edges to the graph G , we are able to obtain the crossing numbers of the join product with the discrete graph D n for two new graphs.

Emotion Recognition Based on Mining Sub-Graphs of Facial Components

Facial emotion recognition finds many real applications in the daily life like human robot interaction, eLearning, healthcare, customer services etc. The task of facial emotion recognition is not easy due to the difficulty in determining the effective feature set that can recognize the emotion conveyed within the facial expression accurately. Graph mining techniques are exploited in this paper to solve facial emotion recognition problem. After determining positions of facial landmarks in face region, twelve different graphs are constructed using four facial components to serve as a source for sub-graphs mining stage using gSpan algorithm. In each group, the discriminative set of sub-graphs are selected and fed to Deep Belief Network (DBN) for classification purpose. The results obtained from the different groups are then fused using Naïve Bayes classifier to make the final decision regards the emotion class. Different tests were performed using Surrey Audio-Visual Expressed Emotion (SAVEE) database and the achieved results showed that the system gives the desired accuracy (100%) when fusion decisions of the facial groups. The achieved result outperforms state-of-the-art results on the same database.

Method of the Joint Clustering in Network and Correlation Spaces

Network algorithms are often used to analyze and interpret the biological data. One of the widely used approaches is to solve the problem of identifying an active module, where a connected subnetwork of a biological network is selected which best reflects the difference between the two considered biological conditions. In this work this approach is extended to the case of a larger number of biological conditions and the problem of the joint clustering in network and correlation spaces is formulated.To solve this problem, an iterative method is proposed at takes as the input graph G and matrix X, in which the rows correspond to the vertices of the graph. As the output, the algorithm produces a set of subgraphs of the graph G so that each subgraph is connected and the rows corresponding to its vertices have a high pairwise correlation. The efficiency of the method is confirmed by an experimental study on the simulated data.

Decompositions of Complete Multigraphs into Cyclic Designs

Let  and  be positive integer,  denote a complete multigraph. A decomposition of a graph  is a set of subgraphs of  whose edge sets partition the edge set of . The aim of this paper, is to decompose a complete multigraph  into cyclic -cycle system according to specified conditions. As the main consequence, construction of decomposition of  into cyclic Hamiltonian wheel system, where , is also given. The difference set method is used to construct the desired designs.

Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star

Abstract Let S n 2 be the graph obtained by the strong prism of a star Sn, i.e. the strong product of K2 and Sn. In this paper, explicit expressions for Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning tress of S n 2 are determined, respectively. More specially, let S n , r 2 be the set of subgraphs obtained by randomly deleting r vertical edges from S n 2 , where 0 ≤ r ≤ n. Explicit formulas for Kirchhoff index and number of spanning trees for any graph S n , r 2 ∈ S n , r 2 are established, respectively. Moreover, the Kirchhoff index of S n , r 2 is almost three-eighths of its Wiener index.

Structure Fault-tolerance of Arrangement Graphs

Given a connected graph G and a connected subgraph H of G. The H-structure connectivity κ(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,J2,…,Jm} in G, where Ji ≅H (1 ≤ i ≤ m), and the deletion of F disconnects G. Similarly, the H-substructure connectivity κs(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,…,Jm} in G, where Ji (1 ≤ i ≤ m) is isomorphic to a connected subgraph of H, and the deletion of F disconnects G. Structure connectivity and substructure connectivity generalize the classical vertex-connectivity. In this thesis, we establish κ(An,k; H) and κs(An,k; H) of the (n, k)-arrangement graph An,k, where H∈{K1,m1,Pm2}(m1≥1,m2≥4).

More Flexible Integration of Functional Systems After Musical Training in Young Adults.

Musical training, because it involves the interaction and integration of diverse functional systems, is an excellent model to investigate training-induced brain plasticity. The human brain functions in a network architecture in which dynamic modules and subgraphs are considered to enable efficient information communication. However, it remains largely unknown how the dynamic integration of functional systems changes with musical training, which may provide new insight into musical training-induced brain plasticity and further the use of music therapy for neuropsychiatric disease and brain injury. Here, 29 healthy young adult novices who received 24 weeks of piano training, and another 27 novices without any intervention were scanned at three time points-before and after musical training and 12 weeks after training. We used nonnegative matrix factorization to identify a set of subgraphs and their corresponding time-dependent coefficients from a concatenated functional network of all the subjects in sliding time windows. The energy and entropy of the time-dependent coefficients were computed to quantify the subgraph's dynamic changes in expression. The training group showed a significantly increased energy of the time-dependent coefficients of 3 subgraphs after training. Furthermore, one of the subgraphs, comprised of primary functional systems and cingulo-opercular task control and salience systems, showed significantly changed entropy in the training group after training. Our results suggest that the integration of functional systems undergoes increased flexibility in fine-scale dynamics after musical training, which reveals how brain functional systems engage in musical performance. The efficacy of musical training induced brain plasticity may provide new therapeutic strategies for brain injury and neuropsychiatric disorders.

Determining crossing numbers of the join products of two specific graphs of order six with the discrete graph

The main aim of the paper is to give the crossing number of the join product G* + Dn for the connected graph G* of order six consisting of P4 + D1 and of one leaf incident with some inner vertex of the path P4 on four vertices, and where Dn consists of n isolated vertices. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G* onto the set of subgraphs by which the edges of G* are crossed exactly once. Due to the mentioned algebraic topological approach, we are able to extend known results concerning crossing numbers for join products of new graphs. The proofs are done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all (k-1)! vertices of the graph. Finally, by adding one edge to the graph G*, we are able to obtain the crossing number of the join product of one other graph with the discrete graph Dn.

ON THE CROSSING NUMBER OF THE JOIN OF THE WHEEL ON FIVE VERTICES WITH THE DISCRETE GRAPH

We give the crossing number of the join product$W_{4}+D_{n}$, where$W_{4}$is the wheel on five vertices and$D_{n}$consists of$n$isolated vertices. The proof is based on calculating the minimum number of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph$W_{4}$and from the set of subgraphs which cross the edges of$W_{4}$exactly once.

Structure and substructure connectivity of circulant graphs and hypercubes

Let H be a connected subgraph of a connected graph G. The H-structure connectivity of the graph G, denoted by κ(G;H), is the minimum cardinality of a minimal set of subgraphs F={H1′,H2′,…,Hm′} in G, such that every Hi′∈F is isomorphic to H and removal of F from G will disconnect G. The H-substructure connectivity of the graph G, denoted by κs(G;H), is the minimum cardinality of a minimal set of subgraphs F={J1′,J2′,…,Jm′} in G, such that every Ji′∈F is a connected subgraph of H and removal of F from G will disconnect G. In this paper, we provide the H-structure and the H-substructure connectivity of the circulant graph Cir(n,Ω) where Ω={1,…,k,n−k,…,n−1},1≤k≤⌊n2⌋ and the hypercube Qn for some connected subgraphs H.

Cluster Tracking Performance Analysis of Linear Heterogeneous Multi-Agent Networks: A Complex Frequency Domain Approach

This paper presents a complex frequency domain approach to investigate the cluster tracking performance of linear heterogeneous multi-agent networks. Firstly, a designed graph matrix is given to eliminate the interaction influence between coupled subnetworks with different tracking signals. On this basis, the cluster tracking performance analysis problem is decomposed into two parts, i.e., stability analysis and steady-state performance analysis of multi-agent networks. Secondly, based on the network structure, a minimum separable subgraph set is proposed to transform the stability of the multi-agent network into the stability of the separable subnetworks. Further, a signal flow diagram is introduced to solve the stability of the separable subnetworks. Thirdly, in view of Final-value theorem, a necessary and sufficient condition is proposed for achieving the cluster tracking control for the closed-loop stable multi-agent network. This result provides a strong theoretical basis for the flexible design of controllers due to that it quantitatively reveals the inherent law of steady-state performance for multi-agent networks. Finally, an algorithm is established to calculate the steady-state error of a general directed multi-agent network. Some simulations are provided to demonstrate the effectiveness of the theoretical results.

Structure connectivity and substructure connectivity of twisted hypercubes

Let G be a graph and T a certain connected subgraph of G. The T-structure connectivity κ(G;T) (or resp., T-substructure connectivity κs(G;T)) of G is the minimum number of a set of subgraphs F={T1,T2,…,Tm} (or resp., F={T1′,T2′,…,Tm′}) such that Ti is isomorphic to T (or resp., Ti′ is a connected subgraph of T) for every 1≤i≤m, and F's removal will disconnect G. The twisted hypercube Hn is a new variant of hypercubes with asymptotically optimal diameter introduced by Zhu. In this paper, we will determine both κ(Hn;T) and κs(Hn;T) for T∈{K1,r,Pk}, respectively, where 3≤r≤4 and 1≤k≤n.