API Reference¶
brainconn.centrality: Centrality¶
Metrics which identify the most important nodes in graphs.
brainconn.centrality |
Metrics which identify the most important nodes in graphs. |
brainconn.centrality.betweenness_bin(G) |
Node betweenness centrality is the fraction of all shortest paths in the network that contain a given node. |
brainconn.centrality.betweenness_wei(G) |
Node betweenness centrality is the fraction of all shortest paths in the network that contain a given node. |
brainconn.centrality.diversity_coef_sign(W, ci) |
The Shannon entropy-based diversity coefficient measures the diversity of intermodular connections of individual nodes and ranges from 0 to 1. |
brainconn.centrality.edge_betweenness_bin(G) |
Edge betweenness centrality is the fraction of all shortest paths in the network that contain a given edge. |
brainconn.centrality.edge_betweenness_wei(G) |
Edge betweenness centrality is the fraction of all shortest paths in the network that contain a given edge. |
brainconn.centrality.eigenvector_centrality_und(CIJ) |
Eigenector centrality is a self-referential measure of centrality: nodes have high eigenvector centrality if they connect to other nodes that have high eigenvector centrality. |
brainconn.centrality.erange(CIJ) |
Shortcuts are central edges which significantly reduce the characteristic path length in the network. |
brainconn.centrality.flow_coef_bd(CIJ) |
Computes the flow coefficient for each node and averaged over the network, as described in Honey et al. |
brainconn.centrality.gateway_coef_sign(W, ci) |
The gateway coefficient is a variant of participation coefficient. |
brainconn.centrality.kcoreness_centrality_bd(CIJ) |
The k-core is the largest subgraph comprising nodes of degree at least k. |
brainconn.centrality.kcoreness_centrality_bu(CIJ) |
The k-core is the largest subgraph comprising nodes of degree at least k. |
brainconn.centrality.module_degree_zscore(W, ci) |
The within-module degree z-score is a within-module version of degree centrality. |
brainconn.centrality.pagerank_centrality(A, d) |
The PageRank centrality is a variant of eigenvector centrality. |
brainconn.centrality.participation_coef(W, ci) |
Participation coefficient is a measure of diversity of intermodular connections of individual nodes. |
brainconn.centrality.participation_coef_sign(W, ci) |
Participation coefficient is a measure of diversity of intermodular connections of individual nodes. |
brainconn.centrality.subgraph_centrality(CIJ) |
The subgraph centrality of a node is a weighted sum of closed walks of different lengths in the network starting and ending at the node. |
brainconn.clustering: Clustering¶
Metrics which group nodes within graphs into clusters.
brainconn.clustering |
Metrics which group nodes within graphs into clusters. |
brainconn.clustering.agreement(ci[, buffsz]) |
Takes as input a set of vertex partitions CI of dimensions [vertex x partition]. |
brainconn.clustering.agreement_weighted(ci, wts) |
D = AGREEMENT_WEIGHTED(CI,WTS) is identical to AGREEMENT, with the exception that each partitions contribution is weighted according to the corresponding scalar value stored in the vector WTS. |
brainconn.clustering.clustering_coef_bd(A) |
The clustering coefficient is the fraction of triangles around a node (equiv. |
brainconn.clustering.clustering_coef_bu(G) |
The clustering coefficient is the fraction of triangles around a node (equiv. |
brainconn.clustering.clustering_coef_wd(W) |
The weighted clustering coefficient is the average “intensity” of triangles around a node. |
brainconn.clustering.clustering_coef_wu(W) |
The weighted clustering coefficient is the average “intensity” of triangles around a node. |
brainconn.clustering.clustering_coef_wu_sign(W) |
Returns the weighted clustering coefficient generalized or separated for positive and negative weights. |
brainconn.clustering.consensus_und(D, tau[, …]) |
This algorithm seeks a consensus partition of the agreement matrix D. |
brainconn.clustering.get_components(A[, …]) |
Returns the components of an undirected graph specified by the binary and undirected adjacency matrix adj. |
brainconn.clustering.get_components_old(A[, …]) |
Returns the components of an undirected graph specified by the binary and undirected adjacency matrix adj. |
brainconn.clustering.number_of_components(A) |
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brainconn.clustering.transitivity_bd(A) |
Transitivity is the ratio of ‘triangles to triplets’ in the network. |
brainconn.clustering.transitivity_bu(A) |
Transitivity is the ratio of ‘triangles to triplets’ in the network. |
brainconn.clustering.transitivity_wd(W) |
Transitivity is the ratio of ‘triangles to triplets’ in the network. |
brainconn.clustering.transitivity_wu(W) |
Transitivity is the ratio of ‘triangles to triplets’ in the network. |
brainconn.core: Core¶
Metrics which identify the most important nodes in graphs.
brainconn.core |
Metrics which identify the most important nodes in graphs. | ||
brainconn.core.assortativity_bin(CIJ[, flag]) |
The assortativity coefficient is a correlation coefficient between the degrees of all nodes on two opposite ends of a link. | ||
brainconn.core.assortativity_wei(CIJ[, flag]) |
The assortativity coefficient is a correlation coefficient between the strengths (weighted degrees) of all nodes on two opposite ends of a link. | ||
brainconn.core.core_periphery_dir(W[, gamma, C0]) |
The optimal core/periphery subdivision is a partition of the network into two nonoverlapping groups of nodes, a core group and a periphery group. | ||
brainconn.core.kcore_bd(CIJ, k[, peel]) |
The k-core is the largest subnetwork comprising nodes of degree at least k. | ||
brainconn.core.kcore_bu(CIJ, k[, peel]) |
The k-core is the largest subnetwork comprising nodes of degree at least k. | ||
brainconn.core.local_assortativity_wu_sign(W) |
Local assortativity measures the extent to which nodes are connected to nodes of similar strength. | ||
brainconn.core.rich_club_bd(CIJ[, klevel]) |
The rich club coefficient, R, at level k is the fraction of edges that connect nodes of degree k or higher out of the maximum number of edges that such nodes might share. | ||
brainconn.core.rich_club_bu(CIJ[, klevel]) |
The rich club coefficient, R, at level k is the fraction of edges that connect nodes of degree k or higher out of the maximum number of edges that such nodes might share. | ||
brainconn.core.rich_club_wd(CIJ[, klevel]) |
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brainconn.core.rich_club_wu(CIJ[, klevel]) |
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brainconn.core.score_wu(CIJ, s) |
The s-core is the largest subnetwork comprising nodes of strength at least s. |
brainconn.degree: Degree¶
Metrics which identify the most important nodes in graphs.
brainconn.degree |
Metrics which identify the most important nodes in graphs. |
brainconn.degree.degrees_dir(CIJ) |
Node degree is the number of links connected to the node. |
brainconn.degree.degrees_und(CIJ) |
Node degree is the number of links connected to the node. |
brainconn.degree.jdegree(CIJ) |
This function returns a matrix in which the value of each element (u,v) corresponds to the number of nodes that have u outgoing connections and v incoming connections. |
brainconn.degree.strengths_dir(CIJ) |
Node strength is the sum of weights of links connected to the node. |
brainconn.degree.strengths_und(CIJ) |
Node strength is the sum of weights of links connected to the node. |
brainconn.degree.strengths_und_sign(W) |
Node strength is the sum of weights of links connected to the node. |
brainconn.distance: Distance¶
Metrics which identify the most important nodes in graphs.
brainconn.distance |
Metrics which identify the most important nodes in graphs. |
brainconn.distance.breadthdist(CIJ) |
The binary reachability matrix describes reachability between all pairs of nodes. |
brainconn.distance.breadth(CIJ, source) |
Implementation of breadth-first search. |
brainconn.distance.charpath(D[, …]) |
The characteristic path length is the average shortest path length in the network. |
brainconn.distance.cycprob(Pq) |
Cycles are paths which begin and end at the same node. |
brainconn.distance.distance_bin(G) |
The distance matrix contains lengths of shortest paths between all pairs of nodes. |
brainconn.distance.distance_wei(G) |
The distance matrix contains lengths of shortest paths between all pairs of nodes. |
brainconn.distance.distance_wei_floyd(adjacency) |
Computes the topological length of the shortest possible path connecting every pair of nodes in the network. |
brainconn.distance.retrieve_shortest_path(s, …) |
Returns nodes comprising shortest path between s and t |
brainconn.distance.efficiency_bin(G[, local]) |
The global efficiency is the average of inverse shortest path length, and is inversely related to the characteristic path length. |
brainconn.distance.efficiency_wei(Gw[, local]) |
The global efficiency is the average of inverse shortest path length, and is inversely related to the characteristic path length. |
brainconn.distance.findpaths(CIJ, qmax, sources) |
Paths are sequences of linked nodes, that never visit a single node more than once. |
brainconn.distance.findwalks(CIJ) |
Walks are sequences of linked nodes, that may visit a single node more than once. |
brainconn.distance.mean_first_passage_time(…) |
Calculates mean first passage time of adjacency |
brainconn.distance.reachdist(CIJ[, …]) |
The binary reachability matrix describes reachability between all pairs of nodes. |
brainconn.distance.search_information(adjacency) |
Calculates search information of adjacency. |
brainconn.generative: Generative¶
Metrics which identify the most important nodes in graphs.
brainconn.generative |
Metrics which identify the most important nodes in graphs. |
brainconn.generative.generative_model(A, D, …) |
Generates synthetic networks using the models described in Betzel et al. |
brainconn.generative.evaluate_generative_model(A, …) |
Generates synthetic networks with parameters provided and evaluates their energy function. |
brainconn.modularity: Modularity¶
Metrics which identify the most important nodes in graphs.
brainconn.modularity |
Metrics which identify the most important nodes in graphs. |
brainconn.modularity.ci2ls(ci) |
Convert from a community index vector to a 2D python list of modules The list is a pure python list, not requiring numpy. |
brainconn.modularity.ls2ci(ls[, zeroindexed]) |
Convert from a 2D python list of modules to a community index vector. |
brainconn.modularity.community_louvain(W[, …]) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes which maximizes the number of within-group edges and minimizes the number of between-group edges. |
brainconn.modularity.link_communities(W[, …]) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes which maximizes the number of within-group edges and minimizes the number of between-group edges. |
brainconn.modularity.modularity_dir(A[, …]) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_finetune_dir(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_finetune_und(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_finetune_und_sign(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_louvain_dir(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_louvain_und(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_louvain_und_sign(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_probtune_und_sign(W) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_und(A[, …]) |
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges. |
brainconn.modularity.modularity_und_sign(W, ci) |
This function simply calculates the signed modularity for a given partition. |
brainconn.modularity.partition_distance(cx, cy) |
This function quantifies the distance between pairs of community partitions with information theoretic measures. |
brainconn.motifs: Motifs¶
Metrics which identify the most important nodes in graphs.
brainconn.motifs |
Metrics which identify the most important nodes in graphs. |
brainconn.motifs.find_motif34(m[, n]) |
This function returns all motif isomorphs for a given motif id and class (3 or 4). |
brainconn.motifs.make_motif34lib() |
This function generates the motif34lib.mat library required for all other motif computations. |
brainconn.motifs.motif3funct_bin(A) |
Functional motifs are subsets of connection patterns embedded within anatomical motifs. |
brainconn.motifs.motif3funct_wei(W) |
Functional motifs are subsets of connection patterns embedded within anatomical motifs. |
brainconn.motifs.motif3struct_bin(A) |
Structural motifs are patterns of local connectivity. |
brainconn.motifs.motif3struct_wei(W) |
Structural motifs are patterns of local connectivity. |
brainconn.motifs.motif4funct_bin(A) |
Functional motifs are subsets of connection patterns embedded within anatomical motifs. |
brainconn.motifs.motif4funct_wei(W) |
Functional motifs are subsets of connection patterns embedded within anatomical motifs. |
brainconn.motifs.motif4struct_bin(A) |
Structural motifs are patterns of local connectivity. |
brainconn.motifs.motif4struct_wei(W) |
Structural motifs are patterns of local connectivity. |
brainconn.physical_connectivity: Physical connectivity¶
Metrics which identify the most important nodes in graphs.
brainconn.physical_connectivity |
Metrics which identify the most important nodes in graphs. |
brainconn.physical_connectivity.density_dir(CIJ) |
Density is the fraction of present connections to possible connections. |
brainconn.physical_connectivity.density_und(CIJ) |
Density is the fraction of present connections to possible connections. |
brainconn.physical_connectivity.rentian_scaling(A, …) |
Physical Rentian scaling (or more simply Rentian scaling) is a property of systems that are cost-efficiently embedded into physical space. |
brainconn.reference: Reference¶
Metrics which identify the most important nodes in graphs.
brainconn.reference |
Metrics which identify the most important nodes in graphs. |
brainconn.reference.latmio_dir_connected(R, itr) |
This function “latticizes” a directed network, while preserving the in- and out-degree distributions. |
brainconn.reference.latmio_dir(R, itr[, D]) |
This function “latticizes” a directed network, while preserving the in- and out-degree distributions. |
brainconn.reference.latmio_und_connected(R, itr) |
This function “latticizes” an undirected network, while preserving the degree distribution. |
brainconn.reference.latmio_und(R, itr[, D]) |
This function “latticizes” an undirected network, while preserving the degree distribution. |
brainconn.reference.makeevenCIJ(n, k, sz_cl) |
This function generates a random, directed network with a specified number of fully connected modules linked together by evenly distributed remaining random connections. |
brainconn.reference.makefractalCIJ(mx_lvl, …) |
This function generates a directed network with a hierarchical modular organization. |
brainconn.reference.makerandCIJdegreesfixed(…) |
This function generates a directed random network with a specified in-degree and out-degree sequence. |
brainconn.reference.makerandCIJ_dir(n, k) |
This function generates a directed random network |
brainconn.reference.makerandCIJ_und(n, k) |
This function generates an undirected random network |
brainconn.reference.makeringlatticeCIJ(n, k) |
This function generates a directed lattice network with toroidal boundary counditions (i.e. |
brainconn.reference.maketoeplitzCIJ(n, k, s) |
This function generates a directed network with a Gaussian drop-off in edge density with increasing distance from the main diagonal. |
brainconn.reference.null_model_dir_sign(W[, …]) |
This function randomizes an directed network with positive and negative weights, while preserving the degree and strength distributions. |
brainconn.reference.null_model_und_sign(W[, …]) |
This function randomizes an undirected network with positive and negative weights, while preserving the degree and strength distributions. |
brainconn.reference.randmio_dir(R, itr) |
This function randomizes a directed network, while preserving the in- and out-degree distributions. |
brainconn.reference.randmio_dir_connected(R, itr) |
This function randomizes a directed network, while preserving the in- and out-degree distributions. |
brainconn.reference.randmio_dir_signed(R, itr) |
This function randomizes a directed weighted network with positively and negatively signed connections, while preserving the positive and negative degree distributions. |
brainconn.reference.randmio_und(R, itr) |
This function randomizes an undirected network, while preserving the degree distribution. |
brainconn.reference.randmio_und_connected(R, itr) |
This function randomizes an undirected network, while preserving the degree distribution. |
brainconn.reference.randmio_und_signed(R, itr) |
This function randomizes an undirected weighted network with positive and negative weights, while simultaneously preserving the degree distribution of positive and negative weights. |
brainconn.reference.randomize_graph_partial_und(A, …) |
A = RANDOMIZE_GRAPH_PARTIAL_UND(A,B,MAXSWAP) takes adjacency matrices A and B and attempts to randomize matrix A by performing MAXSWAP rewirings. |
brainconn.reference.randomizer_bin_und(R, alpha) |
This function randomizes a binary undirected network, while preserving the degree distribution. |
brainconn.similarity: Similarity¶
Metrics which identify the most important nodes in graphs.
brainconn.similarity |
Metrics which identify the most important nodes in graphs. |
brainconn.similarity.corr_flat_dir(a1, a2) |
Returns the correlation coefficient between two flattened adjacency matrices. |
brainconn.similarity.corr_flat_und(a1, a2) |
Returns the correlation coefficient between two flattened adjacency matrices. |
brainconn.similarity.dice_pairwise_und(a1, a2) |
Calculates pairwise dice similarity for each vertex between two matrices. |
brainconn.similarity.edge_nei_overlap_bd(CIJ) |
This function determines the neighbors of two nodes that are linked by an edge, and then computes their overlap. |
brainconn.similarity.edge_nei_overlap_bu(CIJ) |
This function determines the neighbors of two nodes that are linked by an edge, and then computes their overlap. |
brainconn.similarity.gtom(adj, nr_steps) |
The m-th step generalized topological overlap measure (GTOM) quantifies the extent to which a pair of nodes have similar m-th step neighbors. |
brainconn.similarity.matching_ind(CIJ) |
For any two nodes u and v, the matching index computes the amount of overlap in the connection patterns of u and v. |
brainconn.similarity.matching_ind_und(CIJ0) |
M0 = MATCHING_IND_UND(CIJ) computes matching index for undirected graph specified by adjacency matrix CIJ. |
brainconn.nbs: Network-based statistic¶
Network-based statistic calculation.
brainconn.nbs |
Network-based statistic calculation. |
brainconn.nbs.nbs_bct(x, y, thresh[, k, …]) |
Performs the NBS for populations X and Y for a t-statistic threshold of alpha. |
brainconn.utils: Utility functions¶
Utility functions.
brainconn.utils |
Utility functions. |
brainconn.utils.matrix |
Other utility functions. |
brainconn.utils.visualization |
Tools for visualizing graphs. |
brainconn.utils.misc |
Miscellaneous utility functions. |