a 1b4@spdZddlmZddlZddlmZddlmZddl m Z gdZ dd d Z e d e d dd dZ e ZdS)z8Functions for detecting communities based on modularity.) defaultdictN) modularity) MappedQueue)not_implemented_for)greedy_modularity_communities#naive_greedy_modularity_communities$_naive_greedy_modularity_communitiesc sB|}|}|dks ||kr4td|d|||}d||rfdd|j|dD}fdd|j|dD}nfdd|j|dD}}td d |j|dd D]<\} } } | | krq| | | 7<| | | 7<q D]P\} } | D]>\} } | ||| || || || | | <qqfd d|Dt fd d|D} dd|D}t | |kr0z| \}} } Wnt yYq0Yn0| }|  t | dkr| | jd| jd| | fkrZ| | | f| | | ft | dkrl| | jdn| | | f|dkrzq0t|| || B|| <|| =t| }t| }||B| | h}||@}|D]d}||vr| || |}nl||vr2| |||| |||||| }n0| |||| |||||| }| |f|| ffD]\}}|}|||<t |dkr|jd}nd}||f}| }||vr|j|||dn|j||d|dur| j||dn.|jd}||ks |j|jkrr| ||qrq̈| D]}|| }|| =|| kr<|| f| |ffD]h\}}|}||f}|jd|kr||| |t |dkr| |jdn ||qpq<| =t | <|| || 7<d|| <|r|| || 7<d|| <qt|t ddS)a Find communities in G using greedy modularity maximization. This function uses Clauset-Newman-Moore greedy modularity maximization [2]_. Greedy modularity maximization begins with each node in its own community and joins the pair of communities that most increases modularity until no such pair exists or until number of communities `n_communities` is reached. This function maximizes the generalized modularity, where `resolution` is the resolution parameter, often expressed as $\gamma$. See :func:`~networkx.algorithms.community.quality.modularity`. Parameters ---------- G : NetworkX graph weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. resolution : float (default=1) If resolution is less than 1, modularity favors larger communities. Greater than 1 favors smaller communities. n_communities: int Desired number of communities: the community merging process is terminated once this number of communities is reached, or until modularity can not be further increased. Must be between 1 and the total number of nodes in `G`. Default is ``1``, meaning the community merging process continues until all nodes are in the same community or until the best community structure is found. Returns ------- partition: list A list of frozensets of nodes, one for each community. Sorted by length with largest communities first. Examples -------- >>> from networkx.algorithms.community import greedy_modularity_communities >>> G = nx.karate_club_graph() >>> c = greedy_modularity_communities(G) >>> sorted(c[0]) [8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] See Also -------- modularity References ---------- .. [1] Newman, M. E. J. "Networks: An Introduction", page 224 Oxford University Press 2011. .. [2] Clauset, A., Newman, M. E., & Moore, C. "Finding community structure in very large networks." Physical Review E 70(6), 2004. .. [3] Reichardt and Bornholdt "Statistical Mechanics of Community Detection" Phys. Rev. E74, 2006. .. [4] Newman, M. E. J."Analysis of weighted networks" Physical Review E 70(5 Pt 2):056131, 2004. r z$n_communities must be between 1 and z. 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This implementation is O(n^4), much slower than alternatives, but it is provided as an easy-to-understand reference implementation. Greedy modularity maximization begins with each node in its own community and joins the pair of communities that most increases modularity until no such pair exists. This function maximizes the generalized modularity, where `resolution` is the resolution parameter, often expressed as $\gamma$. See :func:`~networkx.algorithms.community.quality.modularity`. Parameters ---------- G : NetworkX graph resolution : float (default=1) If resolution is less than 1, modularity favors larger communities. Greater than 1 favors smaller communities. weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. Returns ------- list A list of sets of nodes, one for each community. Sorted by length with largest communities first. Examples -------- >>> from networkx.algorithms.community import \ ... naive_greedy_modularity_communities >>> G = nx.karate_club_graph() >>> c = naive_greedy_modularity_communities(G) >>> sorted(c[0]) [8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] See Also -------- greedy_modularity_communities modularity css|]}t|gVqdSrr$)r rr r r "rz6naive_greedy_modularity_communities..N)r5rrr css|]}t|dkr|VqdS)rN)r)r cr r rrANrTr') listZnodesr enumeraterr%minappendr2)r4r5rr<ZmergesZold_modularityZnew_modularityZtrial_communitiesZto_mergeirjrZtrial_modularityrr r rrsB2    $    r)Nr r )r N)__doc__ collectionsrZnetworkxZnxZ%networkx.algorithms.community.qualityrZnetworkx.utils.mapped_queuerZnetworkx.utilsr__all__rrrr r r rs     ``