用Networkx实现不同层数的六方晶格

2022-03-31 00:00:00 python networkx graph-theory

问题描述

如何扩展此代码,以包括不同数量的六角形层? 我需要一个给定层数m的六角形点阵的图表。M=1表示1个边为1、中心位于原点的正六边形,对于m=2,在初始正六边形周围添加6个正六边形,对于m=3,添加第三层六边形,依此类推。

import networkx as nx
import matplotlib.pyplot as plt
G = nx.hexagonal_lattice_graph(m=2,n=3, periodic=False, with_positions=True, 
                               create_using=None)
pos = nx.get_node_attributes(G, 'pos')
nx.draw(G, pos=pos, with_labels=True)
plt.show()

解决方案

一个有趣的问题!我花的时间比我预想的要长一点。基本上,函数hexagonal_lattice_graph()生成一个m x n矩形六边形网格。因此,任务是首先绘制一个大网格,然后删除位于最外层之外的节点。 我使用距离来决定保留哪些节点,删除哪些节点。这更加棘手,因为奇数和偶数m的行为略有不同。因此,必须仔细计算中心坐标。

import networkx as nx
import matplotlib.pyplot as plt


def node_dist(x,y, cx, cy):
    """Distance of each node from the center of the innermost layer"""
    return abs(cx-x) + abs(cy-y)


def remove_unwanted_nodes(G, m):
    """Remove all the nodes that don't belong to an m-layer hexagonal ring."""
    
    #Compute center of all the hexagonal rings as cx, cy
    cx, cy = m-0.5, 2*m -(m%2) #odd is 2m-1, even is 2m
    
    #in essence, we are converting from a rectangular grid to a hexagonal ring... based on distance.
    unwanted = []
    for n in G.nodes:    
        x,y = n
        #keep short distance nodes, add far away nodes to the list called unwanted
        if node_dist(x,y, cx, cy) > 2*m:
            unwanted.append(n)

    #now we are removing the nodes from the Graph
    for n in unwanted:
        G.remove_node(n)
        
    return G



##################
m = 4 #change m here. 1 = 1 layer, single hexagon.
G = nx.hexagonal_lattice_graph(2*m-1,2*m-1, periodic=False, 
                               with_positions=True, 
                               create_using=None)
pos = nx.get_node_attributes(G, 'pos')
G = remove_unwanted_nodes(G, m)

#render the result
plt.figure(figsize=(9,9)) 
nx.draw(G, pos=pos, with_labels=True)
plt.axis('scaled')
plt.show()

这将为m=3生成以下内容:

对于m=4:

欢迎来到So!希望上面的解决方案是明确的,并帮助您继续前进。

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