Graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. The combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. This paper presents a Charged System Search (CSS) algorithm for the free shape optimizations of thin-wall...

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

The graph structures of molecules can be a rich source of information about their biological activity or chemical reactivity – however, very efficient methods are required for analyzing them. Due to its complexity, any representation of a chemical database can only convey some characteristics of the whole graph corpus. Additionally, the interesting patterns emerge only from the whole set of gra...

Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by us...

This thesis describes a family of graph-spectral methods for computer vision that exploit the properties of the first eigenvector of the adjacency matrix of a weighted graph. The algorithms are applied to segmentation and grouping, shape-from-shading and graphmatching. In Chapter 3, we cast the problem of grouping into an evidence combining setting where the number of clusters is determined by ...

These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester. Spectral graph techniques are remarkably broad, they are widely-applicable and often very useful, and they also come with a rich underlying theory, some of which provides a very good guide to practice. Spectral graph theory is often ...

Traditional image segmentation is the process of subdividing an image into smaller regions based on some notion of homogeneity or cohesiveness among groups of pixels. Several prominent traditional seg-mentation algorithms have been based on graph theoretic methods [1, 2, 3, 4, 5, 6]. However, these methods have been notoriously difficult to quantitatively evaluate since there is no formal defin...

In this paper we introduce a Hopf algebraic framework for studying invariants of graphs, matroids, and other combinatorial structures. We begin by defining a category of objects, called Whitney systems, which are set systems having the minimum amount of structure necessary in order to have a sensible notion of connected subset, and which generalize graphs and matroids in several ways. Associate...