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NetworkX

A graph created with NetworkX
Original author(s)	Aric Hagberg Pieter Swart Dan Schult
Developer(s)	Many others
Initial release	11 April 2005 (2005-04-11)
Written in	Python
Operating system	Cross-platform
Type	Software library
License	BSD-new license
Website	networkx.github.io

NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license.

History

NetworkX began development in 2002 by Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart. It is supported by the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory.

The package was crafted with the aim of creating tools to analyze data and intervention strategies for controlling the epidemic spread of disease, while also exploring the structure and dynamics of more general social, biological, and infrastructural systems.

Inspired by Guido van Rossum's 1998 essay on Python graph representation, NetworkX made its public debut at the 2004 SciPy annual conference. In April of 2005, NetworkX was made available as open source software.

Several Python packages focusing on graph theory, including igraph, graph-tool, and numerous others, are available. As of April 2024, NetworkX had over 50 million downloads, surpassing the download count of the second most popular package, igraph, by more than 50-fold. This substantial adoption rate could potentially be attributed to NetworkX's early release and its continued evolution within the SciPy ecosystem.

In 2008, SageMath, an open source mathematics system, incorporated NetworkX into its package and added support for more graphing algorithms and functions.

Major NetworkX Releases

Version	Release Date	Major Changes
0.22	17 June 2005	Topological sorting for testing directed acyclic graphs (DAGs). Integration of Dijkstra's algorithm for finding shortest paths in weighted graphs.
0.99	18 November 2008	Default graph type transitioned to a weighted graph. MultiGraph, MultiDiGraph, LabeledGraph, and LabeledDiGraph introduced.
1.0	8 January 2010	Addition of difference and intersection operators. Implementation of the A* algorithm for optimized pathfinding. Incorporation of PageRank, HITS, and [eigenvector] centrality algorithms for network analysis. Integration of Kruskal’s algorithm for constructing minimum spanning trees.
2.0	20 September 2017	Significant revisions to the methods within the MultiGraph and DiGraph classes. Overhaul of documentation system. Various user quality of life changes.
3.0	7 January 2023	Improved integrations to SciPy ecosystem packages. Added new plugin feature to allow users to use different backends (GraphBLAS, CuGraph) for computation.

Features

• Classes for graphs and digraphs.
• Conversion of graphs to and from several formats.
• Ability to construct random graphs or construct them incrementally.
• Ability to find subgraphs, cliques, k-cores.
• Explore adjacency, degree, diameter, radius, center, betweenness, etc.
• Draw networks in 2D and 3D.

Supported Graph Types

Overview

Graphs, in this context, represent collections of vertices (nodes) and edges (connections) between them. NetworkX provides support for several types of graphs, each suited for different applications and scenarios.

Directed Graphs (DiGraph)

Directed graphs, or DiGraphs, consist of nodes connected by directed edges. In a directed graph, edges have a direction indicating the flow or relationship between nodes.

Directed graph made using NetworkX

Undirected Graphs (Graph)

Undirected graphs, simply referred to as graphs in NetworkX, are graphs where edges have no inherent direction. The connections between nodes are symmetrical, meaning if node A is connected to node B, then node B is also connected to node A.

Undirected graph made using NetworkX

MultiGraphs

MultiGraphs allow multiple edges between the same pair of nodes. In other words, MultiGraphs permit parallel edges, where more than one edge can exist between two nodes.

MultiGraph made using NetworkX

MultiDiGraphs

MultiDiGraphs are directed graphs that allow multiple directed edges between the same pair of nodes. Similar to MultiGraphs, MultiDiGraphs enable the modeling of scenarios where multiple directed relationships exist between nodes.

MultiDiGraph made using NetworkX

Suitability

NetworkX is suitable for operation on large real-world graphs: e.g., graphs in excess of 10 million nodes and 100 million edges. Due to its dependence on a pure-Python "dictionary of dictionary" data structure, NetworkX is a reasonably efficient, very scalable, highly portable framework for network and social network analysis.

Applications

NetworkX was designed to be easy to use and learn, as well as a powerful and sophisticated tool for network analysis. It is used widely on many levels, ranging from computer science and data analysis education to large-scale scientific studies.

NetworkX has applications in any field that studies data as graphs or networks, such as mathematics, physics, biology, computer science and social science. The nodes in a NetworkX graph can be specialized to hold any data, and the data stored in edges is arbitrary, further making it widely applicable to different fields. It is able to read in networks from data and randomly generate networks with specified qualities. This allows it to be used to explore changes across wide amounts of networks. The figure below demonstrates a simple example of the software's ability to create and modify variations across large amounts of networks.

Graph representations of several spanning tree networks in Karger's algorithm

NetworkX has many network and graph analysis algorithms, aiding in a wide array of data analysis purposes. One important example of this is its various options for shortest path algorithms. The following algorithms are included in NetworkX, with time complexities given the number of vertices (V) and edges (E) in the graph:

• Dijkstra: O((V+E) log V)
• Bellman-Ford: O(V * E)
• Goldberg-Radzik: O(V * E)
• Johnson: O(V^2 log(V) + VE)
• Floyd Warshall: O(V^3)
• A*: O((V+E) log V)

An example of the use of NetworkX graph algorithms can be seen in a 2018 study, in which it was used to analyze the resilience of livestock production networks to the spread of epidemics. The study used a computer model to predict and study trends in epidemics throughout American hog production networks, taking into account all livestock industry roles. In the study, NetworkX was used to find information on degree, shortest paths, clustering, and k-cores as the model introduced infections and simulated their spread. This was then used to determine which networks are most susceptible to epidemics.

In addition to network creation and analysis, NetworkX also has many visualization capabilities. It provides hooks into Matplotlib and GraphViz for 2D visuals, and VTK and UbiGraph for 3D visuals. This makes the package useful in easily demonstrating and reporting network analysis and data, and allows for the simplification of networks for visual processing.

Integration

NetworkX is integrated into SageMath.

See also

• Social network analysis software
• JGraph

External links

• Official website: networkx.github.io
• NetworkX discussion group
• Survey of existing graph theory software
• NetworkX on StackOverflow
• networkx on GitHub