Skip to content
/ gefura Public

gefura - Python module for measuring brokerage between groups in a network

License

Notifications You must be signed in to change notification settings

rafguns/gefura

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

63 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

gefura

Test with tox codecov

gefura is a small Python module that implements gefura measures, i.e. indicators that characterize to what extent a node forms a 'bridge' between groups in a network. Its name derives from Old Greek γεφυρα, meaning bridge.

These measures are adaptations of betweenness centrality where only shortest paths between nodes from different groups are taken into account. Previously they were known as Q-measures. Because Q is already used for many other concepts (e.g. modularity in networks), we have chosen the new name gefura.

This module implements global and local gefura. Both directed and undirected, as well as weighted and unweighted networks are supported.

gefura only depends on NetworkX.

Definition

Global gefura is an indicator of brokerage between all groups in the network. The global gefura measure (unnormalized) of node $a$ is defined as

$$\Gamma_G(a) = \sum_{g, h \in V, group(g) \neq group(h)} \frac{p_{g,h}(a)}{p_{g,h}}$$

where $p_{g,h}$ is the number of shortest paths between nodes $g$ and $h$, and $p_{g,h}(a)$ is the number of shortest paths between $g$ and $h$ that pass through $a$ ($g \neq h\neq a$).

Local gefura is an indicator of brokerage between a node's own group and all other groups. If node $a$ belongs to group $A$, its local gefura measure (unnormalized) is

$$\Gamma_L(a) = \sum_{g \in A, h \notin A} \frac{p_{g,h}(a)}{p_{g,h}}$$

Example

>>> import networkx as nx
>>> from gefura import global_gefura
>>> G = nx.path_graph(5)
>>> groups = [{0, 2}, {1}, {3, 4}]
>>> global_gefura(G, groups)
{0: 0.0, 1: 0.5, 2: 0.8, 3: 0.6, 4: 0.0}

About

gefura - Python module for measuring brokerage between groups in a network

Topics

Resources

License

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published

Languages