Fast unfolding of communities in large networks

Fast unfolding of communities in large networks

25 Jul 2008 | Vincent D. Blondel1:a, Jean-Loup Guillaume1,2:b, Renaud Lambiotte1,3:c and Etienne Lefebvre1
This paper introduces a fast algorithm for detecting community structures in large networks. The method is based on modularity optimization and is shown to outperform other community detection methods in terms of computation time. It is effective in identifying communities in large networks, such as a Belgian mobile phone network with 2.6 million customers and a web graph with 118 million nodes and over a billion links. The algorithm is also validated on ad-hoc modular networks and is found to be accurate and efficient. The algorithm consists of two phases that are repeated iteratively. In the first phase, communities are identified by optimizing modularity through local changes. In the second phase, a new network is built where the nodes are the previously identified communities. This process is repeated until no further improvements in modularity can be made. The algorithm is able to uncover a hierarchical community structure, allowing for different resolutions of community detection. The algorithm is efficient due to its ability to quickly compute modularity gains and its capacity to reduce the number of communities rapidly. It is also able to circumvent the resolution limit problem of modularity optimization by incorporating a multi-level structure. The algorithm is tested on various networks, including a small social network, a network of scientific papers, a sub-network of the internet, and two large web networks. It is shown to outperform other community detection methods in terms of both speed and modularity. The algorithm is applied to a Belgian mobile phone network, where it successfully identifies communities based on language. The results show that most communities are monolingual, with a high degree of linguistic homogeneity. The algorithm also reveals a hierarchy of communities, with the top-level communities containing over 100 customers. The results suggest that the algorithm can be used to analyze the structure of complex networks and to uncover hierarchical community structures. The algorithm is also shown to be effective in identifying sub-communities and to provide insights into the social cohesion and potential fragility of a country.This paper introduces a fast algorithm for detecting community structures in large networks. The method is based on modularity optimization and is shown to outperform other community detection methods in terms of computation time. It is effective in identifying communities in large networks, such as a Belgian mobile phone network with 2.6 million customers and a web graph with 118 million nodes and over a billion links. The algorithm is also validated on ad-hoc modular networks and is found to be accurate and efficient. The algorithm consists of two phases that are repeated iteratively. In the first phase, communities are identified by optimizing modularity through local changes. In the second phase, a new network is built where the nodes are the previously identified communities. This process is repeated until no further improvements in modularity can be made. The algorithm is able to uncover a hierarchical community structure, allowing for different resolutions of community detection. The algorithm is efficient due to its ability to quickly compute modularity gains and its capacity to reduce the number of communities rapidly. It is also able to circumvent the resolution limit problem of modularity optimization by incorporating a multi-level structure. The algorithm is tested on various networks, including a small social network, a network of scientific papers, a sub-network of the internet, and two large web networks. It is shown to outperform other community detection methods in terms of both speed and modularity. The algorithm is applied to a Belgian mobile phone network, where it successfully identifies communities based on language. The results show that most communities are monolingual, with a high degree of linguistic homogeneity. The algorithm also reveals a hierarchy of communities, with the top-level communities containing over 100 customers. The results suggest that the algorithm can be used to analyze the structure of complex networks and to uncover hierarchical community structures. The algorithm is also shown to be effective in identifying sub-communities and to provide insights into the social cohesion and potential fragility of a country.
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