Graph Spectral Properties Research Articles

Topological properties, entropies, stabilities and spectra of armchair versus zigzag coronene-like nanoribbons

A coronene-like graphitic nanoribbon was recently synthesised as a potential candidate for applications in nanoelectornics due to its unique structural characteristics in contrast with other nanomaterials. It is a planar, thin, finite, and quasi-one-dimensional carbon-based material with novel characteristics. The coronene-like graphitic nanoribbon is constructed using multiple units of a finite dimensional coronene structure linked together in a chain of armchair and zigzag isomers. In this article, we compute the topological properties based on distance and degrees of armchair and zigzag nanoribbon isomers by adopting the orthogonal partition techniques. Our results on entropy measures demonstrate that armchair and zigzag nanoribbon isomers exhibit isentropic structures. We have computed the vertex partitions, C NMR and ESR spectra using distance degree sequence vectors and spectra of armchair and zigzag isomers. Furthermore graph spectral properties of the two isomers are computed which reveal that the zigzag nanoribbons are kinetically more stable than the corresponding armchair isomers.

Face Recognition Through Symbolic Modeling of Face Graphs and Texture

Face recognition helps in authentication of the user using remotely acquired facial information. The dynamic nature of face images like pose, illumination, expression, occlusion, aging, etc. degrades the performance of the face recognition system. In this paper, a new face recognition system using facial images with illumination variation, pose variation and partial occlusion is presented. The facial image is described as a collection of three complete connected graphs and these graphs are represented as symbolic objects. The structural characteristics, i.e. graph spectral properties, energy of graph, are extracted and embedded in a symbolic object. The texture features from the cheeks portions are extracted using center symmetric local binary pattern (CS-LBP) descriptor. The global features of the face image, i.e. length and width, are also extracted. Further symbolic data structure is constructed using the above features, namely, the graph spectral properties, energy of graph, global features and texture features. User authentication is performed using a new symbolic similarity metric. The performance is investigated by conducting the experiments with AR face database and VTU-BEC-DB multimodal database. The experimental results demonstrate an identification rate of 95.97% and 97.20% for the two databases.

Graph Spectral Properties of the Sidechain Networks of Protein Structures: Implications to Allostery and Structure Comparison

Graph Spectral Properties of the Sidechain Networks of Protein Structures: Implications to Allostery and Structure Comparison

Identification of crucial elements for network integrity: a perturbation approach through graph spectral method

The complex behaviour of a network emerges as a product of all the interactions between its components as a single entity. The aim of system level investigations has been to identify emergent properties of a network. Identifying crucial components which are responsible for maintaining integrity of networks is essential, to understand or control them. This study presents a method to rank the participation of nodes and edges in a network using perturbation analysis to identify crucial players that contribute to the integrity of the network. The spectra of a network capture maximal features with minimal loss of information. Unlike earlier methods which evaluate perturbation in a network, based on the change in centralities or paths, the present method uses a network comparison score (Network Similarity Score) which quantifies changes at edge level to global entity level using graph spectral properties. The method is evaluated on realistic complex networks of protein structures of Muscarinic acetylcholine receptors. The important amino acid residues (nodes) and their interactions (edges) derived from the study have been correlated with experimental findings. The potential of perturbation score as a predictive tool for any real-world network is also discussed.

Synchronization Conditions for a Multirate Kuramoto Network With an Arbitrary Topology and Nonidentical Oscillators.

This paper presents methods to find a positively invariant set (PIS) and derive conditions on the edge weights for a multirate Kuramoto oscillator network to achieve synchronization. These methods can be applied to a network with an arbitrary topology and nonidentical oscillators. The proposed methods are based on the construction of energy functions for this type of network. Two different conditions on the edge weights are provided by using graph spectral properties, or alternatively by analyzing a path set of a graph. These methods provide flexibility in checking the edge weight conditions. We further improve the estimate of the PIS for the multirate Kuramoto network when its damping coefficients are greater than a certain value. The effectiveness and conservativeness of the proposed methods are demonstrated by simulation studies. A comparison with another method from the existing literature shows that our method gives less conservative estimate of the PIS.

Pre-emptive spectral graph protection strategies on multiplex social networks

Constructing effective and scalable protection strategies over epidemic propagation is a challenging issue. It has been attracting interests in both theoretical and empirical studies. However, most of the recent developments are limited to the simplified single-layered networks. Multiplex social networks are social networks with multiplelayers where the same set of nodes appear in different layers. Consequently, a single attack can trigger simultaneous propagation in all corresponding layers. Therefore, suppressing propagation in multiplex topologies is more challenging given the fact that each layer also has a different structure. In this paper, we address the problem of suppressing the epidemic propagation in multiplex social networks by allocating protection resources throughout different layers. Given a multiplex graph, such as a social network, and k budget of protection resources, we aim to protect a set of nodes such that the percentage of survived nodes at the end of epidemics is maximized. We propose MultiplexShield, which employs the role of graph spectral properties, degree centrality and layer-wise stochastic propagation rate to pre-emptively select k nodes for protection. We also comprehensively evaluate our proposal in two different approaches: multiplex-based and layer-based node protection schemes. Furthermore, two kinds of common attacks are also evaluated: random and targeted attack. Experimental results show the effectiveness of our proposal on real-world datasets.

Graph Frequency Analysis of Brain Signals.

This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different levels of task familiarity.

A Local Structural Descriptor for Image Matching via Normalized Graph Laplacian Embedding.

This paper investigates graph spectral approaches to the problem of point pattern matching. Specifically, we concentrate on the issue of how to effectively use graph spectral properties to characterize point patterns in the presence of positional jitter and outliers. A novel local spectral descriptor is proposed to represent the attribute domain of feature points. For a point in a given point-set, weight graphs are constructed on its neighboring points and then their normalized Laplacian matrices are computed. According to the known spectral radius of the normalized Laplacian matrix, the distribution of the eigenvalues of these normalized Laplacian matrices is summarized as a histogram to form a descriptor. The proposed spectral descriptor is finally combined with the approximate distance order for recovering correspondences between point-sets. Extensive experiments demonstrate the effectiveness of the proposed approach and its superiority to the existing methods.

Exchangeable Pairs, Switchings, and Random Regular Graphs

We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics for random regular graphs. Previous results on the distribution of cycle counts by McKay, Wormald, and Wysocka (2004) used the method of switchings, a combinatorial technique for asymptotic enumeration. Our proof uses Stein's method of exchangeable pairs and demonstrates an interesting connection between the two techniques.

Expanded Borel Cayley Graphs (Ex-BCGs): A novel communication topology for multi-agent systems

In our early work, we reported Borel Cayley Graphs (BCGs) have the best topological and graph-spectral properties compared to toroidal and diagonal mesh networks and small-world networks. However, BCGs' dependence on generating parameters in size selection and network characteristics has been a challenge in network applications. In this paper, we propose Expanded Borel Cayley Graphs (Ex-BCGs) as a communication topology for multi-agent systems. Ex-BCGs are group-theoretically expanded graphs from BCGs with fixed generating parameters. Ex-BCGs not only conserve constant nodal degree and node labeling scheme but also inherit the communication efficiency of the original BCGs. With experimental results, we show the proposed Ex-BCGs no longer require new generating parameters for new sizes. Moreover, we show resolution of this constraint to produce efficient topological and graph-spectral properties and fast convergence speed when compared to BCGs of similar sizes. We also present the Cut-Through Rewiring (CTR) algorithm as a fault-tolerant methodology against node-failures by regarding pruning nodes as node-failures and utilizing the CTR as a way of recovering connections for neighbors of the pruned nodes in multi-agent systems. The numerical results show that resized networks from Ex-BCGs by the CTR algorithm are more fault-tolerant with robust connectivity, efficient topological properties and faster convergence speed than BCGs.

Intra and Inter-Molecular Communications Through Protein Structure Network

Communication within and across proteins is crucial for the biological functioning of proteins. Experiments such as mutational studies on proteins provide important information on the amino acids, which are crucial for their function. However, the protein structures are complex and it is unlikely that the entire responsibility of the function rests on only a few amino acids. A large fraction of the protein is expected to participate in its function at some level or other. Thus, it is relevant to consider the protein structures as a completely connected network and then deduce the properties, which are related to the global network features. In this direction, our laboratory has been engaged in representing the protein structure as a network of non-covalent connections and we have investigated a variety of problems in structural biology, such as the identification of functional and folding clusters, determinants of quaternary association and characterization of the network properties of protein structures. We have also addressed a few important issues related to protein dynamics, such as the process of oligomerization in multimers, mechanism of protein folding, and ligand induced communications (allosteric effect). In this review we highlight some of the investigations which we have carried out in the recent past. A review on protein structure graphs was presented earlier, in which the focus was on the graphs and graph spectral properties and their implementation in the study of protein structure graphs/networks (PSN). In this article, we briefly summarize the relevant parts of the methodology and the focus is on the advancement brought out in the understanding of protein structure-function relationships through structure networks. The investigations of structural/biological problems are divided into two parts, in which the first part deals with the analysis of PSNs based on static structures obtained from x-ray crystallography. The second part highlights the changes in the network, associated with biological functions, which are deduced from the network analysis on the structures obtained from molecular dynamics simulations.

Virtual identification of essential proteins within the protein interaction network of yeast

Topological analysis of large scale protein-protein interaction networks (PINs) is important for understanding the organizational and functional principles of individual proteins. The number of interactions that a protein has in a PIN has been observed to be correlated with its indispensability. Essential proteins generally have more interactions than the nonessential ones. We show here that the lethality associated with removal of a protein from the yeast proteome correlates with different centrality measures of the nodes in the PIN, such as the closeness of a protein to many other proteins, or the number of pairs of proteins which need a specific protein as an intermediary in their communications, or the participation of a protein in different protein clusters in the PIN. These measures are significantly better than random selection in identifying essential proteins in a PIN. Centrality measures based on graph spectral properties of the network, in particular the subgraph centrality, show the best performance in identifying essential proteins in the yeast PIN. Subgraph centrality gives important structural information about the role of individual proteins, and permits the selection of possible targets for rational drug discovery through the identification of essential proteins in the PIN.

A graph spectral analysis of the structural similarity network of protein chains

We present a simple method for the analysis of large networks based on their graph spectral properties. One of the advantages of this method is that it uses a single numerical computation to identify subclusters in a connected graph, which can significantly simplify the complexity involved in analyzing large graphs. This is illustrated using a network of protein chains constructed on the basis of their structural similarities. The large-scale network properties and the cluster and subcluster organization of the protein chain network are presented. We summarize the results of structural and functional analyses of the nodes present in these clusters and elucidate the implications of structural similarity in the protein chain universe.