directed graphand the previous one introducedundirected graphIt's basically the same, the only difference isdirected graphThe edges of have directionality, which represents a unidirectional or dependent relationship between vertices.
directed graphGGenerally expressed as:G=<V,E>. As with undirected graphs, theVis the set of vertices ofEis the set of edges.
The difference is thatundirected graphis enclosed in parentheses(V,E)，directed graphangle brackets < ><V,E>。
existdirected graphin which the edges are oriented, so that, from theVertex A to Vertex BThe side of the edge with the edge from theVertex B to Vertex AThe side ofnot the sameThe.
together withundirected graphSame.directed graphThere are also many application scenarios, for example:
existMap navigationMiddle.directed graphOften used to represent road networks.
Nodes represent locations (e.g., intersections, cities, etc.), directed edges represent roads, and the weights of the edges can indicate the length of the road, travel time, or traffic conditions.
existchain managementIn this, a directed graph can be used to represent the flow path of goods.
The nodes represent the links in the supply chain (e.g., suppliers, manufacturers, distributors, etc.), the edges represent the paths through which the goods flow, and the capacity of the edges can represent the carrying capacity of the goods.
existsocial networkIn the previous article, it was mentioned that buddy relationships between users can be represented by undirected graphs.
And directed graphs can also be used in social network analysis, it can be used to represent the attention relationship between users, retweeting relationship, etc., used to analyze the user's behavioral patterns.
following introductionmanimPlottingdirected graphtarget audienceDiGraph。
1. Main parameters
directed graph object (math)DiGraphThe main parameters are similar to the undirected graph:
| Parameter name | typology | clarification |
|---|---|---|
| vertices | list | List of vertices of the graph |
| edges | list | The list of edges of the graph, each |
| labels | dict | Whether the vertex displays labeled text |
| label_fill_color | str | Background color of the label |
| layout | str | Layout of the fixed points in the diagram |
| layout_config | dict | Configure how to layout the vertices in the graph |
| layout_scale | float | The scale of the graph's individual vertex layouts |
| vertex_type | Mobject | The type of the vertex, which does not have to be a point, but can be any other object in manim |
| vertex_config | dict | Vertex-related configurations |
| vertex_mobjects | dict | A series of vertex objects |
| edge_type | Mobject | The type of the edge, which does not have to be a line, but can be any other object in the manim |
| edge_config | dict | Edge-related configurations |
| paritions | list | |
| root_vertex | dict |
Of these parameters, theverticescap (a poem)edgesThe related parameters (e.g. xxx_type, xxx_config) are better understood.
labelsparameter sets whether the label of the vertex needs to be displayed or not, the default is to put theverticesvalue as the content of the label.
layoutThe parameters have a variety of ready-made layouts built in:
'circular','kamada_kawai''partite''planar''random''shell''spectral''spiral''spring''tree'
layout_configParameters can be fine-tuned for the above ready-made layout.
The last two parametersparitionscap (a poem)root_vertexMore specific.
paritionscan only be found inlayoutset to'partite'used when generating layered graphs (such as those describing neural networks), the
paritionsUsed to set which vertices each layer contains;
root_vertexcan only be found inlayoutset to'tree'when used for tree diagrams.
root_vertexUsed to set the root node of the tree.
The examples that follow demonstrate how to use theparitionscap (a poem)root_vertexto generatebedded (geology)cap (a poem)tree-like(used form a nominal expression)directed graph。
2. Main approaches
directed graphDiGraphmethods are mainly used to dynamically change directed graphs, such as adding or removing vertices and edges.
| name (of a thing) | clarification |
|---|---|
| add_edges | Adding edges to a directed graph |
| add_vertices | Adding vertices to a directed graph |
| remove_edges | Deleting edges of a directed graph |
| remove_vertices | Delete the vertices of a directed graph |
| change_layout | The structure of a dynamically modified directed graph |
| from_networkx | through (a gap)networkxto generate a directed graph |
networkxis another commonly usedPythonlibrary for creating, manipulating, and studying the structure of complex networks.
DiGraphobjects can also be used directly based on thenetworkxof the object generation graph.
3. Examples of use
The following example is similar to the previous example of an undirected graph, except that it uses a directed graph insteadDiGraphobject to implement it.
3.1. Vertex configuration
The setup of vertices is almost the same as for undirected graphs.
# Different color settings
graph = DiGraph(
vertex_config={
0: {"color": RED}, # ...
# ...
},
)
# Vertex display label
graph = DiGraph(
labels=True, )
)
# Star Vertices
graph = DiGraph(
vertex_config={"outer_radius": 0.15}, vertex_type=Star, }
vertex_type=Star, )
)
3.2 Configuration of edges
Like vertices, edges of directed graphs can have color, thickness, and other attributes.
The difference with an undirected graph is that the edges of a directed graph can be styled with arrows.
# Color of the edge
graph = DiGraph(
edge_config={
(0, 1): {"color": RED},
# ...
},
)
# Thickness of the edge
graph = DiGraph(
edge_config={
(0, 1): {"stroke_width": 1},
# ...
},
)
# Sides with different arrows
graph = DiGraph(
edge_config={
(0, 1): {
"tip_config": {
"tip_shape": ArrowCircleTip,
},
},
(0, 2): {
"tip_config": {
"tip_shape": ArrowTriangleTip,
},
},
# ...
},
)
3.3. Built-in layout
directed graphThe built-in layout is the same as the one described in the previous article on undirected graphs.
for layout in [
"spring",
"circular",
"kamada_kawai",
"planar",
"random",
"shell",
"spectral",
"spiral",
]:
graph = DiGraph(
layout=layout,
)
3.4 Layer diagrams
The layout of the cascade diagram needs to be coupled with the parameterpartitionsUsed together, thepartitionsin determining which vertices are in each layer.
Directed graphs have edges that have directions and are plotted more like the structure of a neural network.
partitions = [[0, 1], [2, 3, 4], [5, 6], [7, 8]]
graph = DiGraph(
layout="partite",
partitions=partitions,
)
3.5. Tree diagrams
The layout of the tree diagram needs to work with the parametersroot_vertexUsed together, theroot_vertexdefines the tree'sroot vertexWhich one is it.
This is the same place asundirected graphOne difference is that when drawing a directed tree graph, the order of vertices and edges is important, and you need to start at the root node and pass in each vertex in turn.
In the following example, the second dendrogram changes the root node, not just theroot_vertexJust do it, you need to change the order of the vertices in the graph first.
The code below is abbreviated, the full code can be downloaded from the link in the last part of the text.
# Initial tree
graph = DiGraph(
layout="tree",
root_vertex=0, )
)
# Important!!!!
# The order of nodes and edges needs to be adjusted before modification
# Modify the root node
graph2 = DiGraph(
layout="tree",
root_vertex=2, )
)
4. Annexes
The complete code for the article is on a web disk (），
Download at.Full Code (Access code: 6872)