In my experience using graphviz to render graphs of that size (~ 700 nodes), minimal trial-and-error adjustment to this combination of attribute settings--some structural, some purely aesthetic--for all three objects (graph, nodes, and edges) should do what you want:
reduce the minimum separation between nodes, via 'nodesep'; e.g., nodes[nodesep=0.75]; this will make your graph being "too compact." (nodesep and ranksep probably affect how dot draws a graph more than any other adjustable parameter)
reduce the minimum distance between nodes of different ranks, e.g, nodes[ranksep=0.75]; 'ranksep' sets the minimum distance between nodes of different ranks--this will affect your graph layout significantly if your graph is comprised of many ranks
increase the edge weights, eg, edge[weight=1.2]; this will make the edges shorter, in turn making the entire graph more compact
remove node borders and node fill, e.g., nodes[color=none; shape=plaintext], especially for oval-shaped nodes, a substantial fraction of the total node space is 'unused' (ie, not used to display the node label); each node's footprint is now reduced to just its text
explicitly set the font size for the nodes (the node borders are enlarged so that they surround the node text, which means that the font size and amount of text for a given node has a significant effect on its size); [fontsize=11] should be large enough to be legible yet also reduce the 'cluttered' appearance (the default size is 14)
use different colors for nodes and edges--this will make your graph easier to read; e.g., set the node 'text' fontcolor to blue and the edge fontcolor to "grey" to help the eye distinguish the two sets of graph structures. This will make a bigger difference than you might think.
explicitly set total graph size, eg, graph[size="7.75,10.25"] (ensures that your graph fits on an 8.5 x 11 page and that it occupies the entire space)