Mathematica中的多图形8 [英] Multigraphs in Mathematica 8

问题描述

我只花了几个小时试图转换超过图表的 LayeredDrawing 。

获得3个世界最好的方法是使用 Graph 对象作为图形存储的主要工具，并为 GraphPlot ， Combinatorica 和 GraphUtilities 函数接受图对象

例如：

• 您需要 Combinatorica 或 GraphUtilities - 创建一个包装 someAlgorithm ，它包含 Graph 对象，将其转换到边的列表或> Combinatorica 图（ GraphUtilities'ToCombinatoricaGraph 有帮助），运行al gorithm，将它转换回 Graph 对象，注意设置正确的 GraphStyle 和 VertexCoordinates 来自原始图形对象。由于冲突，确保 Combinatorica 和 GraphUtilities 不在上下文路径中，I 执行使用$ Pre




• 您需要像这里，或多边形图形 - 制作一个包装函数 someGraphPlot ，它接受图对象，将其转换为正确的表示形式，然后使用 GraphPlot 或者可能会创建一个临时图形对象顶点/边缘形状用于这个图的目的。请注意，您可以使用 SetProperty 附加属性到边缘，这样您就可以将多图形存储在 Graph 中。




• 您想使用 GraphPlot 中的一个布局，并将坐标存储在 Graph - 使用像这里从 GraphPlot 布局获取顶点坐标，并使用 VertexCoordinates 来将它们存储在图形 code>




以下是笔记本展示这些使用案例和其他一些案例

I just spent a couple of hours trying to convert some old code that uses Mathematica 7's GraphPlot to use the new Mathematica 8 Graph functions. It seemed sensible since the new graph drawing is much nicer and it has things like AdjacencyMatrix and KirchhoffMatrix built in.

The problem is that I can not figure out how to get graphs with multiple edges to work in Mma 8.

The Feynman graph that I use as my canonical example is the two-loop vacuum graph

GraphPlot[{1 -> 2, 1 -> 2, 1 -> 2}, MultiedgeStyle -> .5, 
          DirectedEdges -> True, VertexCoordinateRules -> {{-1, 0}, {1, 0}}]

Trying to make the similar graph in Mma 8

Graph[{DirectedEdge[1, 2], DirectedEdge[1, 2], DirectedEdge[1, 2]}, 
      VertexCoordinates -> {{-1, 0}, {1, 0}}]

yields the error message

Graph::supp: Mixed graphs and multigraphs are not supported. >>

How can I construct (and work with) a similar graph using Mathematica 8's Graph[] objects?

Edit: This problem still exists in Mathematica 9

解决方案

I went through a similar process of trying to use Graph for everything, and found that it it does not replace Combinatorica and GraphPlot. The best use for Graph is to use it as a container type to store vertices + edges + coordinates.

For example, most of the functions from "Algorithmic Graph Theory" of Combinatorica tutorial are not available for new Graph objects. When I talked with a WRI developer on Graph project, my understanding was providing all of Combinatorica functions for Graph is not a priority because the design goal is to provide methods that solve tasks in algorithmic agnostic way. For instance, you may have method to find vertex cover and graph coloring for new Graph object, but for algorithmic specific tasks like Brelaz coloring and Greedy Vertex Cover, you may always have to defer to Combinatorica.

In addition to multi-graphs, some graph layouts are not available for Graph objects. You can not fix some vertex coordinates and let automatic layout do the rest. Also, layout of LayeredGraphPlot is not available and is sometimes preferred over Graph's LayeredDrawing.

The way to get the best of 3 worlds is to use Graph objects as main vehicle for graph storage and make wrappers for GraphPlot, Combinatorica and GraphUtilities functions that accept Graph objects

Some use cases:

• You need some algorithm from Combinatorica or GraphUtilities -- make a wrapper someAlgorithm that takes Graph object, converts it to list of edges or Combinatorica graph (GraphUtilities'ToCombinatoricaGraph is helpful), runs the algorithm, converts it back to Graph object, taking care to set correct GraphStyle and VertexCoordinates from the original graph object. Because of conflicts, make sure Combinatorica and GraphUtilities are not on context path, I do it using $Pre

• You need some custom graph plot like here, or the multi-edge graph -- make a wrapper function someGraphPlot that accepts Graph object, converts it to correct representation, then uses GraphPlot or perhaps creates a temporary Graph object with custom vertex/edge shapes for the purpose of this one plot. Note that you can attach properties to edges using SetProperty so you can store your multigraphs in Graph that way.

• You want to use one of GraphPlot layouts and store coordinates in Graph -- use function like here to get vertex coordinates from GraphPlot layout, and store them in Graph object using VertexCoordinates

Here's a notebook demonstrating these use cases and a few others

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