Abstract: An apparatus and method for generating connected graphs for display on a computer monitor. A data structure and virtual map are defined which provide a linked list of objects appearing at any location in the connected graph, the virtual map being larger than the dimensions of the display monitor if the connected graph demands larger dimensions. Commands carried out with respect to any object on the monitor are correlated with the cell maps in the virtual map, which point to the linked lists of objects, the lists in turn pointing to objects stored in an object records database. This provides rapid access to all objects at any given location on the display or in the connected graph. When a user gives a command to create a connection between two objects in the graph, the method generates the shortest connection possible, in terms of both pixel length and arc length for arc-connections, balanced against a minimization of collisions by the connection with existing objects, including other connections.