Applications of Graph Theory

Graph-theoretical methods are being increasingly used in areas of interest within the IEEE and beyond. Graphs are mathematical abstractions that can be used to represent networks of various types: physical (e.g., the internet or electrical networks), biological (e.g., brain networks), or social (e.g., online social networks). Furthermore, graphs can provide tools for flexible representation of data sets in which data points have irregular positions with respect to each other. Common examples of this include data sets acquired by a sensor network, where uniform sensor placement may not be possible, or machine learning data sets, where training samples are not uniformly distributed in feature space. In some instances, a graph representation arises as a natural way to describe the problem, while in other areas, e.g., image processing, they are being used to develop powerful, content-dependent alternatives to conventional processing tools.