Month: January 2020

3 follow-up notes on 3 python list comprehension tricks

I saw the following post about list comprehension tricks in Python. I really like python comprehension functionality – dict, set, list, I don’t discriminate. So 3 follow up notes about this post –

1. Set Comprehension

Beside dictionary and lists, comprehensions also work for sets –

{s for s in [1, 2, 1, 0]}
#set(0,1,2))
{s**2 for s in [1,2,1,0,-1]}
#set(0,1,4)

2. Filtering (and a glimpse to generators)

In order to filter a list, one can iterate over the list or generator, apply the filter function and output a list or can use the build-in filter function and receive a generator that is more efficient as described further in the original post.

words = ['deified', 'radar', 'guns']
palindromes = filter(lambda w: w==w[::-1], words)
list(palindromes)
#['deified', 'radar']

Additional nice to know the build-in function is the map function, that for example can yield the words’ lengths as generators – 

words = ['deified', 'radar', 'guns']
lengths = map(lambda w: len(w), words)
list(lengths)
#[7, 5, 4]

3. Generators

Another nice usage of generators is to create an infinite sequence – 


def infinite_sequence():

    num=0

    while True:

        yield num

        num+=1


gen = infinite_sequence()

next(gen)

#0

next(gen)

#1

next(gen)

#2

Generators can be piped, return multiple outputs, and more. I recommend this postto a better understand generators.

 

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3 interesting features of NetworkX

“NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.”

NetworkX lets the user create a graph and then study it. For example – find the shortest path between nodes, find node degree, find the maximal clique, find coloring of a graph and so on. In this post, I’ll present a few features I find interesting and are maybe less known.

Multigraphs

Multigraph is a graph that can store multiedges. Multiedges are multiple edges between two nodes (it is different from hypergraph where an edge can connect any number of nodes and no just two). NetworkX has 4 graph types – the well-known commonly used directed and undirected graph and 2 multigraphs –  nx.MultiDiGraph for directed multigraph and nx.MultiGraph for undirected multigraph.

In the example below, we see that if the graph type is not defined correctly, functionalities such as degree calculation may yield the wrong value –

import networkx as nx</pre>
G = nx.MultiGraph() G.add_nodes_from([1, 2, 3]) G.add_edges_from([(1, 2), (1, 3), (1, 2)]) print(G.degree()) #[(1, 3), (2, 2), (3, 1)] H = nx.Graph() H.add_nodes_from([1, 2, 3]) H.add_edges_from([(1, 2), (1, 3), (1, 2)]) print(H.degree()) #[(1, 2), (2, 1), (3, 1)]

Create a graph from pandas dataframe

Pandas is the swiss knife of every data scientist, so naturally, it would be a good idea to create a graph from pandas dataframe. The other way around is also possible. See the documentation here. The example below shows how to create a multigraph from a pandas dataframe where each edge has a weight property.

import pandas as pd</pre>
df = pd.DataFrame([[1, 1, 4], [2, 1, 5], [3, 2, 6], [1, 1, 3]], columns=['source', 'destination', 'weight']) print(df) # source destination weight # 0 1 1 4 # 1 2 1 5 # 2 3 2 6 # 3 1 1 3 G = nx.from_pandas_edgelist(df, 'source', 'destination', ['weight'], create_using=nx.MultiGraph) print(nx.info(G)) # Name: # Type: MultiGraph # Number of nodes: 3 # Number of edges: 4 # Average degree: 2.6667

Graph generators

One of the features I find the most interesting and powerful. The graph generator interface allows creating several types we just one line of code. Some of the graphs are deterministic given a parameter (e.g complete graph of k nodes) while some are random (e.g. binomial graph). Below are a few examples of deterministic graphs and random graphs. The examples below are the tip of the iceberg of the graph generator capabilities.

Complete graph – creates a graph with n nodes and an edge between every two nodes.

Empty graph – creates a graph with n nodes and no edges.

Star graph – create a graph with one central node connected to n external nodes.

G = nx.complete_graph(n=9)
print(len(G.edges()), len(G.nodes()))
# 36 9
H = nx.complete_graph(n=9, create_using=nx.DiGraph)
print(len(H.edges()), len(H.nodes()))
# 72 9
J = nx.empty_graph(n=9)
print(len(J.edges()), len(J.nodes()))
# 0 9
K = nx.star_graph(n=9)
print(len(K.edges()), len(K.nodes()))
# 9 10

Binomial Graph – create a graph with n nodes and each edge is created with probability p (alias for gnp_random_graph and erdos_renyi_graph).

G1 = nx.binomial_graph(n=9, p=0.5, seed=1)
G2 = nx.binomial_graph(n=9, p=0.5, seed=1)
G3 = nx.binomial_graph(n=9, p=0.5)
print(G1.edges()==G2.edges(), G1.edges()==G3.edges())
# True False

Random regular graph – creates a graph with n nodes, edges are created randomly and each node has degree d.

G = nx.random_regular_graph(d=4, n=10)
nx.draw(G)
plt.show()

Random regula graph

Random tree – create a uniformly random tree of n nodes.

G = nx.random_tree(n=10)
nx.draw(G)
plt.show()

random_tree

All the code in this post can be found here

Additional Resource

Official site

SO questions

https://www.datacamp.com/community/tutorials/networkx-python-graph-tutorial

https://www.geeksforgeeks.org/directed-graphs-multigraphs-and-visualization-in-networkx/amp/