The Application of Machine Learning to Problems in Graph Drawing A Literature Review Raissa dos Santos Vieira Hugo Alexandre Dantas do Nascimento Wanderson Barcelos da Silva Institute of Informatics Federal University of Goi´ as Goiˆ ania - GO, Brazil Email: {raissavieira,hadn,wandersonsilva}@inf.ufg.br Abstract—Graph drawing, as a research field, is concerned with the visualization of information modeled in the form of graphs. The present paper is a literature review that identifies the state- of-the-art in applying machine learning techniques to problems in graph drawing. We focused on machine learning strategies that build up and represent knowledge about how to draw a graph. Surprisingly, only a few pieces of research can be found about this subject. We classified them in two main groups: the ones that extract knowledge from the user by human-computer interaction and those that are not based on data directly gathered from users. The study of these methods shows that there is still much to research and to develop regarding the application of machine learning to graph drawing. We suggest directions for future research on this area. Keywords–Graph Drawing; Human-Computer Interaction; Ma- chine Learning. I. I NTRODUCTION Graphs are mathematical models defined as a set of ver- tices and a set of edges. They are widely used to represent physical and abstract entities and their relationships. Often, it is necessary to draw a graph, that is, to construct a geometric representation of its vertices and edges [1]. For this aim, it is common to choose a standard graph-related convention (for example, drawing vertices as circles and edges as straight lines) and a set of aesthetic criteria (such as displaying edges with uniform orientation, minimizing edge crossings and presenting symmetry). When a graph contains only a few vertices and edges, it can easily be drawn manually. However, as the size of the graph increases, manual drawing becomes more difficult and time consuming. The most common strategy for drawing medium to large-size graphs – ranging from hundreds to thousands of vertices and edges – is through the usage of automated techniques that incorporate a set of aesthetic criteria and apply algorithms for finding aesthetically pleasing drawings. A number of computational systems for drawing graphs exist based on this approach. Including, we have GraphViz [2] and Gephi [3]. Drawing a graph by a computational process, on the other hand, also creates many difficulties. One of them is that the search for drawings of good quality drawings with several aesthetic criteria is an NP-Hard problem [1]. In addition, some aesthetic criteria are in conflict, so that the improvement of a drawing in respect to one criterion may imply a reduction of other aesthetical aspects. Furthermore, the drawing of a graph is essentially a subjective task – some users may prefer to satisfy some particular aesthetic criteria, different from the preferences of other users. For this reason, even with the use of heuristics, there is still a need for human intervention to assist in obtaining good quality graph drawings. This was perceived very early in the advent of the graph drawing research field, resulting in the inclusion of human-computer interactive resources in most graph drawing systems. Such resources help to tailor the drawing towards satisfying aesthetic criteria that are not fully treated computationally, and to escape from local minima, when the graph drawing process involves an optimization model. In the current paper, we present a literature review of the use of machine learning techniques for graph drawing. This is a much more complex challenge than merely having a fully automatic graph drawing system or a system with a few simple interactive tools. We shall comment on computational approaches that attempt to acquire knowledge that can be used to help drawing graphs. As can be seen, there are few reports of research on this subject. However, some interesting ones have been found and their study may lead to promising lines of future research. The remainder of the paper is organized as follows: in Section II, graph drawing definitions are presented; Section III provides an overview of the application of machine learning techniques to graph drawing; Section IV summarizes the characteristics of the existing approaches; finally, in Section V, we draw our conclusions and suggest future works. II. GRAPH DRAWING A finite undirected graph G is an ordered pair (V,E) of finite sets V and E, where V is a set of vertices representing a set of discrete objects, and E is a set of unordered pairs {x, y} of distinct elements in V, termed edges between vertices x and y. In a directed graph, E is a set of ordered pairs of vertices such that an edge e =(x, y) connects x to y, but the reverse is not true, unless there is an edge e 0 =(y,x) in E.A two- dimensional drawing of a graph G =(V,E) is a function that associates each vertex and edge of G with geomtric objects in a drawing space. 112 Copyright (c) IARIA, 2015. ISBN: 978-1-61208-386-5 eKNOW 2015 : The Seventh International Conference on Information, Process, and Knowledge Management