wg dZddlZddlZddlmZdgZededejdd d Zy) z#Computation of graph non-randomnessN)not_implemented_fornon_randomnessdirected multigraphweight) edge_attrsc ddl}tj|rtjdtj|stj dt ttj|dkDrtjd|1t ttjj|}|jjtj||}t|j!|j#|d|}|j%}|j'}d|z|z|||z zz }||d|zz |z|zz t)j*d|z|zd|z zz } || fS) aCompute the non-randomness of graph G. The first returned value nr is the sum of non-randomness values of all edges within the graph (where the non-randomness of an edge tends to be small when the two nodes linked by that edge are from two different communities). The second computed value nr_rd is a relative measure that indicates to what extent graph G is different from random graphs in terms of probability. When it is close to 0, the graph tends to be more likely generated by an Erdos Renyi model. Parameters ---------- G : NetworkX graph Graph must be symmetric, connected, and without self-loops. k : int The number of communities in G. If k is not set, the function will use a default community detection algorithm to set it. 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, i.e., the graph is binary. Returns ------- non-randomness : (float, float) tuple Non-randomness, Relative non-randomness w.r.t. Erdos Renyi random graphs. Raises ------ NetworkXException if the input graph is not connected. NetworkXError if the input graph contains self-loops or if graph has no edges. Examples -------- >>> G = nx.karate_club_graph() >>> nr, nr_rd = nx.non_randomness(G, 2) >>> nr, nr_rd = nx.non_randomness(G, 2, "weight") Notes ----- This computes Eq. (4.4) and (4.5) in Ref. [1]_. If a weight field is passed, this algorithm will use the eigenvalues of the weighted adjacency matrix to compute Eq. (4.4) and (4.5). References ---------- .. [1] Xiaowei Ying and Xintao Wu, On Randomness Measures for Social Networks, SIAM International Conference on Data Mining. 2009 rNz-non_randomness not applicable to empty graphszNon connected graph.z!Graph must not contain self-loops)r)numpynxis_empty NetworkXError is_connectedNetworkXExceptionlenlistselfloop_edgestuple communitylabel_propagation_communitieslinalgeigvalsto_numpy_arrayfloatrealsumnumber_of_nodesnumber_of_edgesmathsqrt) Gkrnp eigenvaluesnrnmpnr_rds g/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/non_randomness.pyrr sX~ {{1~NOO ??1 ""#9:: 4!!!$ %&*BCCy bll@@CD E))##B$5$5a$GHK rwwrvvk"1o./ 0B A A QqAE{#AAAI?Q& '499QUQY!a%5H+I IE u9)Nr) __doc__r networkxr networkx.utilsr__all__ _dispatchablerr,r+r3sV* .  Z \"X&T'#!Tr,