Abstract: A computer-implemented method of drawing an undirected graph in which multiple nodes are connected by multiple edges is provided using a computer system in which a computer is coupled to the computer display. The computer includes a processor and memory. A representation is received of a graph having multiple nodes and multiple edges, in which positions of the nodes relative to one another have been previously determined. The representation is modified so as to: 1) preserve the positions of the nodes relative to one another; and 2) simplify the visual representation of the graph by sharing drawn lines between different distinct edges in such a way as to enable the different distinct edges, despite such sharing, to still be recognized by a user. In one embodiment, the processor places the nodes in unique positions with integer coordinates.

Abstract: A computer-implemented method is provided for drawing a graph in which multiple nodes are connected by multiple edges. An image is displayed representing a node, and the image is processed to distinguish image foreground pixels and image background pixel. An edge is displayed incident to the node, the edge extending over selected background pixels and stopping short of selected foreground pixels. There results a graph drawing that is more aesthetically pleasing.

Abstract: A computer-implemented method is provided for drawing a graph in which multiple nodes are connected by multiple edges. An image is displayed representing a node, and the image is processed to distinguish image foreground pixels and image background pixel. An edge is displayed incident to the node, the edge extending over selected background pixels and stopping short of selected foreground pixels. There results a graph drawing that is more aesthetically pleasing.

Abstract: A system for arranging a plurality of nodes into graphical layout form partitions the nodes into a set of clusters from which a cluster graph is created. The cluster partitioning is based on the inter-nodal relationships, and cluster size depends on the number of nodes associated with each cluster. The clusters are laid out to avoid overlap, and cluster boundaries, within which nodes in a cluster are constrained, are generated. Nodes of each cluster as classified as either internal or boundary nodes, with boundary nodes being projected outward towards the boundary of the cluster. As an optional step, connection edges between nodes are routed to avoid overlap.

Abstract: A method is provided for automated placement of labels for a given graph layout or map. Even though in practice a label is usually associated with a line (edge), point (node) or area, this method can be extended to produce labeling solution for any graphical feature with explicit geometric representation (in two or three dimensions). This method first finds a labeling solution for a set of graphical features G by eliminating a subset of the set of potential label placements for any member of G, and reducing the labeling problem to a maximum matching problem of a bipartite graph. Next, if there are graphical features in G that have no label placement assigned to them yet, a backtracking algorithm may be used to improve the space available for the labeled graphical features. It may be shown that the labeling problem is NP-hard if any graphical feature in G is a line or point. As a result, the GFLP problem cannot be solved in polynomial time, but requires the application of well-devised heuristics.