Louvain Modularity Fast unfolding of communities in large networks

Louvain Modularity

Fast unfolding of communities in large networks

https://arxiv.org/pdf/0803.0476.pdf

【一些算法的思路 都很简单 ；但是数学翻译是严谨的】

【0-全局模块度,原始模块度，全局目标函数1-阶段临时新网络的模块度】

The problem of community detection requires the partition of a network into
communities of densely connected nodes, with the nodes belonging to different
communities being only sparsely connected.

This search
for fast algorithms has attracted much interest in recent years due to the increasing
availability of large network data sets and the impact of networks on every day life.

The quality of the
partitions resulting from these methods is often measured by the so-called modularity
of the partition. The modularity of a partition is a scalar value between -1 and 1
that measures the density of links inside communities as compared to links between
communities [4, 11].

Contrary
to all the other community detection algorithms, the network size limits that we are
facing with our algorithm are due to limited storage capacity rather than limited
computation time: identifying communities in a 118 million nodes network took only
152 minutes [20].