Graphviz - chunhualiao/public-docs GitHub Wiki

GraphViz Layout Algorithms

GraphViz provides several layout algorithms (also called layout engines or programs) besides the default "dot" algorithm. Each is designed for different types of graphs and visualization needs:

Main GraphViz Layout Engines

  1. dot - The default hierarchical layout algorithm for directed graphs

    • Designed for directed graphs and hierarchical data
    • Creates layered drawings with edges pointing in the same direction (typically top to bottom or left to right)
    • Best for: flow charts, hierarchies, dependency trees, organizational charts

  2. neato - Spring model layout (Kamada-Kawai algorithm)

    • Uses a physical simulation of springs to position nodes
    • Creates more organic, force-directed layouts
    • Best for: undirected graphs with a fairly small number of nodes (less than 100)

  3. fdp - Spring model layout (Fruchterman-Reingold algorithm)

    • Another force-directed approach, but with a different algorithm than neato
    • Often produces more spread-out layouts than neato
    • Best for: undirected graphs, medium-sized networks

  4. sfdp - Scalable force-directed placement

    • Multiscale version of fdp designed for larger graphs
    • Uses a multilevel approach to handle graphs with many nodes efficiently
    • Best for: large undirected graphs (hundreds or thousands of nodes)

  5. twopi - Radial layout

    • Places nodes in concentric circles around a central node
    • Distance from center represents graph distance
    • Best for: graphs where the relationship to a central node is important

  6. circo - Circular layout

    • Places nodes in a circle
    • Particularly good for certain network topologies like rings
    • Best for: cyclic structures, ring networks, and some biological pathways

Usage in GraphViz

In the GraphViz command line, you would specify these layouts like:

dot -Tpng -Kdot input.dot -o output.png    # Use dot layout
dot -Tpng -Kneato input.dot -o output.png  # Use neato layout
dot -Tpng -Kfdp input.dot -o output.png    # Use fdp layout

Graphviz and the DOT Language: A Deep Dive into Hierarchical Graph Drawing

Graphviz, an acronym for Graph Visualization Software, is a powerful open-source toolkit for creating graph visualizations. At its core lies the DOT language, a simple yet expressive text-based language for describing graphs. Among its suite of layout engines, the dot program is arguably the most widely recognized, specializing in producing hierarchical, or layered, drawings of directed graphs. This makes it exceptionally well-suited for visualizing structures like flowcharts, dependency graphs, and organizational charts.

This article delves into the intricacies of Graphviz's dot program, exploring its layout algorithm, implementation details, potential performance bottlenecks, and strategies for optimization.

The dot Layout Algorithm: A Four-Phase Approach

The dot layout algorithm is a sophisticated process that transforms a textual DOT graph description into a visually appealing two-dimensional diagram. This process, largely based on the work of Sugiyama, Tagawa, and Toda, can be broken down into four distinct phases:

  1. Cycle Removal: The foundation of the dot algorithm is the assumption that the input graph is a Directed Acyclic Graph (DAG). Since many real-world graphs contain cycles, the first step is to break these cycles by reversing the direction of a carefully selected set of edges. This is a crucial step as it enables the subsequent hierarchical arrangement of nodes.

  2. Rank Assignment: Once the graph is acyclic, dot assigns each node to a discrete rank. In a top-to-bottom layout, these ranks correspond to the y-coordinate of the nodes. The goal of this phase is to create a "proper" ranking, where for every edge from node u to node v, the rank of u is less than the rank of v. To achieve this, long edges that span multiple ranks are broken down into a series of "virtual" nodes and edges of unit length. The primary objective during rank assignment is to minimize the total length of all edges in the graph.

  3. Node Ordering and Crossing Minimization: With nodes assigned to their respective ranks, the next challenge is to arrange them within each rank to minimize the number of edge crossings. This is a notoriously difficult combinatorial problem (NP-complete). The dot program employs a heuristic approach to tackle this. It iteratively sweeps through the ranks, adjusting the order of nodes in one rank based on the positions of their neighbors in the adjacent rank. This process is repeated until a satisfactory ordering with minimal crossings is achieved.

  4. Coordinate Assignment and Edge Routing: In the final phase, the algorithm determines the precise x-coordinates for each node, aiming to keep edges short and straight. This is another optimization problem where the positions of nodes are adjusted to minimize a cost function related to edge lengths and angles. Once the final node positions are set, the paths for the edges are calculated. For straight edges, this is straightforward. However, for edges that are not straight lines (splines), the algorithm calculates a smooth curve that avoids overlapping with other nodes and edges, ensuring a clear and readable final output.

Implementation Details: Under the Hood of dot

The implementation of the dot layout algorithm involves several sophisticated techniques and data structures:

Phase Implementation Details
Rank Assignment dot employs a network simplex algorithm to find an optimal ranking of the nodes. This is a powerful optimization technique borrowed from the field of linear programming that efficiently minimizes the total edge length.
Crossing Minimization The heuristic used for crossing reduction is an iterative barycenter method. For each node, it calculates a "barycenter" which is the average position of its neighbors in the adjacent rank. Nodes within a rank are then reordered based on these barycenter values. This process is applied iteratively, sweeping up and down through the ranks.
Initial Ordering The initial ordering of nodes within a rank can significantly impact the final layout. dot often uses a depth-first or breadth-first search starting from the nodes with the minimum rank to establish an initial, sensible ordering before the crossing minimization phase begins.
Coordinate Assignment The assignment of x-coordinates is modeled as a quadratic optimization problem, which can be solved efficiently. This ensures that nodes are positioned horizontally in a way that minimizes the overall "stretch" of the edges.
Edge Routing For complex edge paths, dot utilizes B-splines, which are piecewise polynomial curves that provide smooth and aesthetically pleasing connections between nodes. The algorithm carefully routes these splines to avoid intersecting with nodes and other edge labels.

Performance Bottlenecks and Optimization Strategies

While the dot algorithm is highly effective for many graphs, it can encounter performance challenges, especially with large and dense graphs. Understanding these bottlenecks is key to creating efficient visualizations.

Common Bottlenecks:

  • Crossing Minimization: As an NP-complete problem, finding the absolute minimum number of edge crossings is computationally expensive. For graphs with many nodes and edges per rank, the iterative heuristic can become a significant performance drag.
  • Large Number of Edges and Virtual Nodes: Graphs with long edges that span many ranks lead to the creation of numerous virtual nodes and edges. This increases the complexity of the internal graph representation and slows down subsequent layout phases.
  • Dense Connectivity: Highly interconnected graphs, where a large percentage of possible edges exist, present a major challenge for the crossing minimization and coordinate assignment phases.
  • Complex Edge Splines: The calculation of smooth, non-overlapping B-splines for a multitude of edges can be computationally intensive, especially in cluttered areas of the graph.

Solutions and Optimization Techniques:

  1. Leverage Alternative Layout Engines: Graphviz provides other layout engines tailored for different graph structures. For undirected graphs, neato and fdp (force-directed placement) can be more suitable and often faster. For very large graphs, sfdp offers a scalable version of fdp. twopi and circo are designed for radial and circular layouts, respectively.

  2. Adjust Graph Attributes: The DOT language offers a rich set of attributes to control the layout process and mitigate performance issues:

    • splines=false;: This is one of the most effective ways to speed up rendering. It forces edges to be drawn as straight lines, eliminating the computationally expensive spline routing phase.
    • nodesep and ranksep: Increasing the values of these attributes provides more space between nodes and ranks, which can sometimes simplify the layout process and improve readability, though it may also increase the overall size of the drawing.
    • nslimit and mclimit: These attributes can be used to control the network simplex algorithm's effort, potentially at the cost of a less optimal layout.

  3. Graph Preprocessing: For extremely large or complex graphs, it can be beneficial to preprocess the graph before feeding it to dot. This could involve:

    • Clustering: Grouping related nodes into subgraphs can simplify the top-level layout.
    • Filtering: Removing less important nodes or edges can significantly reduce the complexity of the graph.

  4. Utilize Modern Tools and Techniques:

    • Web-based Viewers: For interactive exploration of large graphs, web-based libraries like D3.js, often in conjunction with Graphviz for initial layout, can provide a more responsive user experience.
    • Incremental Layout: While not a core feature of the standard dot program, some systems that use Graphviz can implement incremental layout algorithms, where only the changed portions of a graph are re-laid out, saving significant computation time.

In conclusion, Graphviz's dot program remains a cornerstone of graph visualization due to its powerful and well-reasoned layout algorithm. By understanding the principles behind its phased approach, the intricacies of its implementation, and the strategies for navigating its performance limitations, users can effectively harness its capabilities to create clear, informative, and aesthetically pleasing hierarchical visualizations of complex data.