sh:SrS/rSS.SjrSrS\0rSSS.Sjrg) a Local Community Detection Algorithms Local Community Detection (LCD) aims to detected one or a few communities starting from certain source nodes in the network. This differs from Global Community Detection (GCD), which aims to partition an entire network into communities. LCD is often useful when only a portion of the graph is known or the graph is large enough that GCD is infeasable [1]_ Gives a good introduction and overview of LCD References ---------- .. [1] Baltsou, Georgia, Konstantinos Christopoulos, and Konstantinos Tsichlas. Local community detection: A survey. IEEE Access 10 (2022): 110701-110726. https://doi.org/10.1109/ACCESS.2022.3213980 greedy_source_expansionN)cutoffc ^Uc [S5nU1mU1nXR5T- nUVVs1sH'oPRU5Hn[XV/5iM M) nnnUVs1sH!n[ U4SjU55(dMUiM# n nSn [ T5U:aU(dT$Sn Sn [ 5=n =pUH)n[UUTX7U 5unnnnUU :dMUn Un Un UnUnM+ TU 1-mURX R5T- 5 URU 5 U nUnUn X:aT$U n [ T5U:aMT$s snnfs snf)Ninfc3,># UH oT;v M g7fN).0nodeCs w/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/networkx/algorithms/community/local.py 3_clauset_greedy_source_expansion..!s">19) floatkeys neighbors frozensetalllenset)_calculate_local_modularity_for_candidateupdateremove)GsourcerBUr nbrTedgeIR_valuemax_R best_node best_node_B best_node_T best_node_IvR_tmpB_tmpT_tmpI_tmpr s @r _clauset_greedy_source_expansionr.sy ~u A A 1A,-KADT9J#D; 9J AAK?!$s">">>!A?G a&6/ 6 H3 25%7 7kA)R1aq* &E5%u} # # #   O ""$q()     ?  H7 a&6/: HC L?s.E%EEc^X!1-mUR5nUR5nUR5n[5n XHn U T;a,URU5 UR[X/55 X;a@[ U4SjX 55n U (d"UR U 5 U RU 5 U T;dMUR[X/55 M U HKn X H@n X;dM UR [X/55 UR [X/55 MB MM [U5S:a[U5[U5- OSnXXx4$)a Compute the local modularity R and updated variables when adding node v to the community. Parameters ---------- G : NetworkX graph The input graph. v : node The candidate node to add to the community. C : set The current set of community nodes. B : set The current set of boundary nodes. T : set of frozenset The current set of boundary edges. I : set of frozenset The current set of internal boundary edges. Returns ------- R_tmp : float The local modularity after adding node v. B_tmp : set The updated set of boundary nodes. T_tmp : set of frozenset The updated set of boundary edges. I_tmp : set of frozenset The updated set of internal boundary edges. c3,># UH oT;v M g7frr)r nbr_nbrC_tmps r r <_calculate_local_modularity_for_candidate..ss LV'!5Vrr)copyraddranyrdiscardr)rr)r rr r"r+r,r-removed_B_nodesrnbr_still_in_B removed_noderemoved_node_nbrr*r2s @r rrDs.< GE FFHE FFHE FFHEeOt e  IIaL IIi) * 8! LQV LLN! S!##C( %< IIi) *#(( ! , i)9(HIJ i)9(HIJ!0( (+5zA~CJU #1E  %%clauset)rmethodcf[UnU"XUS9$![an[US35UeSnAff=f)u Find the local community around a source node. Find the local community around a source node using Greedy Source Expansion. Greedy Source Expansion generally identifies a local community starting from the source node and expands it based on the criteria of the chosen algorithm. The algorithm is specified with the `method` keyword argument. * `"clauset"` [1]_ uses local modularity gain to determine local communities. The algorithm adds nbring nodes that maximize local modularity to the community iteratively, stopping when no additional nodes improve the modularity or when a predefined cutoff is reached. Local modularity measures the density of edges within a community relative to the total graph. By focusing on local modularity, the algorithm efficiently uncovers communities around a specific node without requiring global optimization over the entire graph. The algorithm assumes that the graph $G$ consists of a known community $C$ and an unknown set of nodes $U$, which are adjacent to $C$ . The boundary of the community $B$, consists of nodes in $C$ that have at least one nbr in $U$. Mathematically, the local modularity is expressed as: .. math:: R = \frac{I}{T} where $T$ is the number of edges with one or more endpoints in $B$, and $I$ is the number of those edges with neither endpoint in $U$. Parameters ---------- G : NetworkX graph The input graph. source : node The source node from which the community expansion begins. cutoff : int, optional (default=None) The maximum number of nodes to include in the community. If None, the algorithm expands until no further modularity gain can be made. method : string, optional (default='clauset') The algorithm to use to carry out greedy source expansion. Supported options: 'clauset'. Other inputs produce a ValueError Returns ------- set A set of nodes representing the local community around the source node. Examples -------- >>> G = nx.karate_club_graph() >>> nx.community.greedy_source_expansion(G, source=16) {16, 0, 4, 5, 6, 10} Notes ----- This algorithm is designed for detecting local communities around a specific node, which is useful for large networks where global community detection is computationally expensive. The result of the algorithm may vary based on the structure of the graph, the choice of the source node, and the presence of ties between nodes during the greedy expansion process. References ---------- .. [1] Clauset, Aaron. Finding local community structure in networks. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 72, no. 2 (2005): 026132. https://arxiv.org/pdf/physics/0503036 z( is not a valid choice for an algorithm.N)rr) ALGORITHMSKeyError ValueError)rrrr?algoes r rrsLVU&!  00 UF8#KLMSTTUs  0+0)__doc____all__r.rrArrr=r rHsB, % %;?' T@&H/ 26iP1r=