Package 'cograph'

Description

Abbreviates labels to a maximum length, adding ellipsis if truncated.

Usage

abbrev_label(label, abbrev = NULL, n_labels = NULL)

label_abbrev(label, abbrev = NULL, n_labels = NULL)

Arguments

Value

Character vector of (possibly abbreviated) labels.

Examples

labels <- c("VeryLongStateName", "Short", "AnotherLongName")

# No abbreviation
abbrev_label(labels, NULL)

# Fixed max length
abbrev_label(labels, 5)  # "Very…", "Short", "Anot…"

# Auto-adaptive
abbrev_label(labels, "auto")

Description

Combines multiple network layers into a single network.

Usage

aggregate_layers(
  layers,
  method = c("sum", "mean", "max", "min", "union", "intersection"),
  weights = NULL
)

lagg(
  layers,
  method = c("sum", "mean", "max", "min", "union", "intersection"),
  weights = NULL
)

Arguments

Value

Aggregated adjacency matrix

Examples

# layers <- list(L1 = mat1, L2 = mat2, L3 = mat3)
# aggregate_layers(layers, "sum")           # Total
# aggregate_layers(layers, "mean")          # Average
# aggregate_layers(layers, "union")         # Any edge
# aggregate_layers(layers, "intersection")  # All edges

Description

Aggregates a vector of edge weights using various methods. Compatible with igraph's edge.attr.comb parameter.

Usage

aggregate_weights(w, method = "sum", n_possible = NULL)

wagg(w, method = "sum", n_possible = NULL)

Arguments

Value

Single aggregated value

Examples

w <- c(0.5, 0.8, 0.3, 0.9)
aggregate_weights(w, "sum")   # 2.5
aggregate_weights(w, "mean")  # 0.625
aggregate_weights(w, "max")   # 0.9

Description

Creates a lightweight cograph_network object from various network inputs. The resulting object is a named list with all data accessible via $.

Usage

as_cograph(x, directed = NULL, simplify = FALSE, ...)

to_cograph(x, directed = NULL, ...)

Arguments

Details

The cograph_network format is designed to be:

• Lean: Only essential data stored, computed values derived on demand

• Modern: Uses named list elements instead of attributes for clean $ access

• Compatible: Works seamlessly with splot() and other cograph functions

Use getter functions for programmatic access: get_nodes, get_edges, get_labels, n_nodes, n_edges

Use setter functions to modify: set_nodes, set_edges, set_layout

Value

A cograph_network object: a named list with components:

nodes

Data frame with id, label, and optional layout or metadata columns

edges

Data frame with from, to, weight columns

directed

Logical indicating if network is directed

weights

Full n×n weight matrix when available for matrix/TNA round-trips, or NULL

data

Original estimation data (sequence matrix, edge list, etc.), or NULL

meta

Consolidated metadata list with sub-fields: source (input type string), layout (layout info list or NULL), tna (TNA metadata or NULL)

node_groups

Optional node groupings data frame

A cograph_network object. See as_cograph.

See Also

get_nodes to extract the nodes data frame, get_edges to extract edges as a data frame, n_nodes and n_edges for counts, is_directed to check directedness, splot for plotting

Examples

mat <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), nrow = 3)
net <- as_cograph(mat)
get_nodes(net)
get_edges(net)
splot(net)
mat <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), nrow = 3)
net <- to_cograph(mat)

Description

Convert various objects to the mcml class – a clean, tna-independent representation of a multilayer cluster network.

Usage

as_mcml(x, ...)

## S3 method for class 'cluster_summary'
as_mcml(x, ...)

## S3 method for class 'group_tna'
as_mcml(x, clusters = NULL, method = "sum", type = "tna", directed = TRUE, ...)

## S3 method for class 'mcml'
as_mcml(x, ...)

## Default S3 method:
as_mcml(x, ...)

Arguments

Value

An mcml object with components macro, clusters, cluster_members, and meta.

An mcml object.

An mcml object. When clusters is provided, macro$data contains the cluster assignments and macro$weights is NULL (the macro is the sequence of clusters, not a summary).

The input mcml object unchanged.

See Also

build_mcml, as_tna

Examples

# From cluster_summary
mat <- matrix(c(0.5, 0.2, 0.3,
                0.1, 0.6, 0.3,
                0.4, 0.1, 0.5), 3, 3, byrow = TRUE,
              dimnames = list(c("A", "B", "C"), c("A", "B", "C")))
clusters <- list(G1 = c("A", "B"), G2 = c("C"))
cs <- cluster_summary(mat, clusters, type = "tna")
m <- as_mcml(cs)
m$macro$weights

Description

Converts a cluster_summary object to proper tna objects that can be used with all functions from the tna package. Creates a macro (cluster-level) tna model and per-cluster tna models (internal transitions within each cluster), returned as a flat group_tna object.

Usage

as_tna(x)

## S3 method for class 'cluster_summary'
as_tna(x)

## S3 method for class 'mcml'
as_tna(x)

## Default S3 method:
as_tna(x)

Arguments

Details

This is the final step in the MCML workflow, enabling full integration with the tna package for centrality analysis, bootstrap validation, permutation tests, and visualization.

Requirements

The tna package must be installed. If not available, the function throws an error with installation instructions.

Workflow

# Full MCML workflow
net <- cograph(edges, nodes = nodes)
net$nodes$clusters <- group_assignments
cs <- cluster_summary(net, type = "tna")
tna_models <- as_tna(cs)

# Now use tna package functions
plot(tna_models$macro)
tna::centralities(tna_models$macro)
tna::bootstrap(tna_models$macro, iter = 1000)

# Analyze per-cluster patterns
plot(tna_models$ClusterA)
tna::centralities(tna_models$ClusterA)

Excluded Clusters

A per-cluster tna cannot be created when:

• The cluster has only 1 node (no internal transitions possible)

• Some nodes in the cluster have no outgoing edges (row sums to 0)

These clusters are silently excluded. The macro (cluster-level) model still includes all clusters.

Value

A group_tna object (S3 class) – a flat named list of tna objects. The first element is named "macro" and represents the cluster-level transitions. Subsequent elements are named by cluster name and represent internal transitions within each cluster.

macro

A tna object representing cluster-level transitions. Contains $weights (k x k transition matrix), $inits (initial distribution), and $labels (cluster names). Use this for analyzing how learners/entities move between high-level groups or phases.

<cluster_name>

Per-cluster tna objects, one per cluster. Each tna object represents internal transitions within that cluster. Contains $weights (n_i x n_i matrix), $inits (initial distribution), and $labels (node labels). Clusters with single nodes or zero-row nodes are excluded (tna requires positive row sums).

A group_tna object (flat list of tna objects: macro + per-cluster).

A group_tna object (flat list of tna objects: macro + per-cluster).

A tna object constructed from the input.

See Also

cluster_summary to create the input object, plot_mcml for visualization without conversion, tna::tna for the underlying tna constructor

Examples

mat <- matrix(runif(36), 6, 6); diag(mat) <- 0
rownames(mat) <- colnames(mat) <- LETTERS[1:6]
clusters <- list(G1 = c("A","B"), G2 = c("C","D"), G3 = c("E","F"))
cs <- cluster_summary(mat, clusters, type = "tna")
tna_models <- as_tna(cs)
names(tna_models)          # "macro", "G1", "G2", "G3"
splot(tna_models$macro)    # cograph renderer avoids tna's plot deps

Description

Computes the degree assortativity coefficient, measuring the tendency of nodes to connect to other nodes with similar degree. Positive values indicate assortative mixing (high-degree nodes connect to high-degree nodes), negative values indicate disassortative mixing.

Usage

assortativity(x, directed = NULL, type = NULL, digits = NULL, ...)

Arguments

Details

The degree assortativity coefficient is defined as the Pearson correlation coefficient between the degrees of nodes at either end of each edge (Newman 2002):

$r = \frac{\sum_{jk} jk(e_{jk} - q_j q_k)}{\sigma_q^2}$

where $e_{jk}$ is the fraction of edges connecting degree-$j$ to degree-$k$ vertices, $q_k$ is the excess degree distribution, and $\sigma_q^2$ its variance.

For directed networks, different degree combinations (in/out) at source and target ends can be specified via the type parameter.

Value

An object of class "cograph_assortativity" with components:

coefficient

Numeric scalar: the assortativity coefficient in $[-1, 1]$.

type

Character: the degree type used.

directed

Logical: whether the network was treated as directed.

n_nodes

Integer: number of nodes.

n_edges

Integer: number of edges.

network

The original input network.

References

Newman, M.E.J. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701. doi:10.1103/PhysRevLett.89.208701

See Also

assortativity_attribute, centrality, network_summary

Examples

# Assortative network (high-degree connect to high-degree)
adj <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 1, 1, 0,
  1, 1, 0, 0, 1,
  1, 1, 0, 0, 1,
  0, 0, 1, 1, 0
), 5, 5)
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
cograph::assortativity(adj)

Description

Computes assortativity with respect to a node attribute, measuring the tendency of nodes to connect to others with similar attribute values. For categorical attributes, this computes the modularity-based nominal assortativity. For numeric attributes, this computes the Pearson correlation between attribute values at edge endpoints.

Usage

assortativity_attribute(x, values, directed = NULL, digits = NULL, ...)

homophily(x, values, directed = NULL, digits = NULL, ...)

Arguments

Details

For categorical (nominal) attributes, the coefficient is:

$r = \frac{\text{tr}(\mathbf{e}) - \|\mathbf{e}^2\|}{1 - \|\mathbf{e}^2\|}$

where $\mathbf{e}$ is the mixing matrix with $e_{ij}$ = fraction of edges connecting type $i$ to type $j$.

For numeric (scalar) attributes, the coefficient is the Pearson correlation between attribute values at edge endpoints.

Value

An object of class "cograph_assortativity" with components:

coefficient

Numeric scalar: assortativity coefficient.

type

Character: "nominal" or "scalar".

directed

Logical.

n_nodes

Integer.

n_edges

Integer.

attribute_values

The attribute values used.

network

Original input.

References

Newman, M.E.J. (2003). Mixing patterns in networks. Physical Review E, 67(2), 026126. doi:10.1103/PhysRevE.67.026126

See Also

assortativity, detect_communities

Examples

adj <- matrix(c(0,1,1,0, 1,0,0,0, 1,0,0,1, 0,0,1,0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
groups <- c(A = "x", B = "x", C = "y", D = "y")
cograph::assortativity_attribute(adj, groups)

Description

Builds a Multi-Cluster Multi-Level (MCML) model from raw transition data (edge lists or sequences) by recoding node labels to cluster labels and counting actual transitions. Unlike cluster_summary which aggregates a pre-computed weight matrix, this function works from the original transition data to produce the TRUE Markov chain over cluster states.

Usage

build_mcml(
  x,
  clusters = NULL,
  method = c("sum", "mean", "median", "max", "min", "density", "geomean"),
  type = c("tna", "frequency", "cooccurrence", "semi_markov", "raw"),
  directed = TRUE,
  compute_within = TRUE
)

Arguments

Value

Usually an mcml object. Existing mcml or cluster_summary inputs are returned unchanged. Transition-data results include meta$source = "transitions" and are compatible with plot_mcml, as_tna, and splot.

See Also

cluster_summary for matrix-based aggregation, as_tna to convert to tna objects, plot_mcml for visualization

Examples

# Edge list with clusters
edges <- data.frame(
  from = c("A", "A", "B", "C", "C", "D"),
  to   = c("B", "C", "A", "D", "D", "A"),
  weight = c(1, 2, 1, 3, 1, 2)
)
clusters <- list(G1 = c("A", "B"), G2 = c("C", "D"))
cs <- build_mcml(edges, clusters)
cs$macro$weights

# Sequence data with clusters
seqs <- data.frame(
  T1 = c("A", "C", "B"),
  T2 = c("B", "D", "A"),
  T3 = c("C", "C", "D"),
  T4 = c("D", "A", "C")
)
cs <- build_mcml(seqs, clusters, type = "raw")
cs$macro$weights

Description

Computes centrality measures for nodes in a network and returns a tidy data frame. Accepts matrices, igraph objects, cograph_network, or tna objects.

Usage

centrality(
  x,
  type = c("basic", "extended", "all"),
  measures = NULL,
  mode = "all",
  normalized = FALSE,
  weighted = TRUE,
  directed = NULL,
  loops = TRUE,
  simplify = "sum",
  digits = NULL,
  sort_by = NULL,
  cutoff = -1,
  invert_weights = NULL,
  alpha = 1,
  damping = 0.85,
  personalized = NULL,
  transitivity_type = "local",
  isolates = "nan",
  lambda = 1,
  diffusion_method = NULL,
  k = 3,
  states = NULL,
  decay_parameter = 0.5,
  dmnc_epsilon = 1.7,
  membership = NULL,
  katz_alpha = 0.1,
  hubbell_weight = 0.5,
  tna_network = NULL,
  psych_network = NULL,
  ...
)

Arguments

Details

The following centrality measures are available:

degree

Count of edges (supports mode: in/out/all)

strength

Weighted degree (supports mode: in/out/all)

betweenness

Shortest path centrality

closeness

Inverse distance centrality (supports mode: in/out/all)

eigenvector

Influence-based centrality

pagerank

Random walk centrality (supports damping and personalization)

authority

HITS authority score

hub

HITS hub score

eccentricity

Maximum distance to other nodes (supports mode)

coreness

K-core membership (supports mode: in/out/all)

constraint

Burt's constraint (structural holes)

transitivity

Local clustering coefficient (supports multiple types)

harmonic

Harmonic centrality - handles disconnected graphs better than closeness (supports mode: in/out/all)

diffusion

Diffusion degree centrality - sum of scaled degrees of node and its neighbors (supports mode: in/out/all, lambda scaling)

leverage

Leverage centrality - measures influence over neighbors based on relative degree differences (supports mode: in/out/all)

kreach

Geodesic k-path centrality - count of nodes reachable within distance k (supports mode: in/out/all, k parameter)

alpha

Alpha/Katz centrality - influence via paths, penalized by distance. Similar to eigenvector but includes exogenous contribution

power

Bonacich power centrality - measures influence based on connections to other influential nodes

subgraph

Subgraph centrality - participation in closed loops/walks, weighting shorter loops more heavily

laplacian

Laplacian centrality using Qi et al. (2012) local formula. Matches NetworkX and centiserve::laplacian()

load

Load centrality - fraction of all shortest paths through node, similar to betweenness but weights paths by 1/count

current_flow_closeness

Information centrality - closeness based on electrical current flow (requires connected graph)

current_flow_betweenness

Random walk betweenness - betweenness based on current flow rather than shortest paths (requires connected graph)

voterank

VoteRank - identifies influential spreaders via iterative voting mechanism. Returns normalized rank (1 = most influential)

percolation

Percolation centrality - importance for spreading processes. Uses node states (0-1) to weight paths. When all states equal, equivalent to betweenness. Useful for epidemic/information spreading analysis.

radiality

Radiality centrality (centiserve). Sum of (diam + 1 - d) normalized by n-1.

lin

Lin's centrality. Reachable nodes squared divided by sum of distances.

decay

Decay centrality. Sum of delta^d for parameter delta.

residual_closeness

Residual closeness. Sum of 1/2^d.

dangalchev

Dangalchev closeness (alias for residual closeness).

generalized_closeness

Generalized closeness. Sum of alpha^d.

harary

Harary centrality. Sum of 1/d^2 for all reachable pairs.

average_distance

Average distance (centiserve). Sum of distances / (n+1).

barycenter

Barycenter centrality. 1 / sum of distances.

wiener

Wiener index. Total sum of shortest path distances from node.

closeness_vitality

Closeness vitality. Drop in Wiener index when node removed.

communicability

Total communicability. Row sums of matrix exponential.

communicability_betweenness

Communicability betweenness. Fraction of communicability through each node.

random_walk

Random walk centrality. Inverse sum of random walk distances (requires connected graph).

stress

Stress centrality. Number of shortest paths through node.

flow_betweenness

Flow betweenness. Max-flow based betweenness.

lobby

Lobby index (h-index of neighborhood).

entropy

Graph entropy centrality. Entropy change on node removal.

semilocal

Semi-local centrality. Triple-nested neighborhood sum.

clusterrank

ClusterRank. Clustering coefficient times neighbor degree sum.

bottleneck

Bottleneck centrality. Count of shortest path trees where node is critical.

centroid

Centroid value. Minimum f(v,i) across all nodes.

mnc

Maximum Neighborhood Component size.

dmnc

Density of Maximum Neighborhood Component.

topological_coefficient

Topological coefficient. Shared neighbor ratio.

bridging

Bridging centrality. Betweenness times bridging coefficient.

local_bridging

Local bridging. (1/degree) times bridging coefficient.

effective_size

Burt's effective size. Degree minus redundancy.

diversity

Diversity centrality. Shannon entropy of edge weight distribution.

cross_clique

Cross-clique connectivity. Count of cliques containing node.

markov

Markov centrality. Inverse mean first passage time (requires connected graph).

integration

Integration centrality. Distance-based influence.

expected

Expected centrality. Sum of neighbor degrees.

gilschmidt

Gil-Schmidt power index. Sum of 1/d normalized by n-1.

salsa

SALSA authority scores (directed graphs only).

leaderrank

LeaderRank. PageRank with ground node (directed graphs only).

participation

Participation coefficient. Diversity of inter-community connections (requires membership).

within_module_z

Within-module degree z-score. Intra-community connectivity (requires membership).

gateway

Gateway coefficient. Inter-community brokerage weighted by centrality (requires membership).

Value

A data frame with columns:

• node: Node labels/names

• One column per measure, with mode suffix for directional measures (e.g., degree_in, closeness_all)

Examples

# Basic usage with matrix
adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality(adj)

# Specific measures
centrality(adj, measures = c("degree", "betweenness"))

# Directed network with normalization
centrality(adj, mode = "in", normalized = TRUE)

# Sort by pagerank
centrality(adj, sort_by = "pagerank", digits = 3)

# PageRank with custom damping
centrality(adj, measures = "pagerank", damping = 0.9)

# Harmonic centrality (better for disconnected graphs)
centrality(adj, measures = "harmonic")

# Global transitivity
centrality(adj, measures = "transitivity", transitivity_type = "global")

Description

Influence via all paths penalized by distance. Similar to eigenvector centrality but includes an exogenous contribution, making it well-defined even for directed acyclic graphs.

Usage

centrality_alpha(x, mode = "all", ...)

Arguments

Value

Named numeric vector of alpha centrality values.

See Also

centrality for computing multiple measures at once, centrality_eigenvector for a related measure.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_alpha(adj)

Description

Kleinberg's HITS algorithm. centrality_authority scores nodes pointed to by good hubs. centrality_hub scores nodes that point to good authorities.

Usage

centrality_authority(x, ...)

centrality_hub(x, ...)

Arguments

Value

Named numeric vector of authority or hub scores.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 0, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_authority(adj)
centrality_hub(adj)

Description

Sum of shortest path distances divided by (n + 1). Lower values indicate more central nodes.

Usage

centrality_average_distance(x, mode = "all", ...)

Arguments

Value

Named numeric vector of average distance values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_average_distance(adj)

Description

Inverse of the total distance to all reachable nodes.

Usage

centrality_barycenter(x, mode = "all", ...)

Arguments

Value

Named numeric vector of barycenter centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_barycenter(adj)

Description

Fraction of shortest paths passing through each node. Nodes with high betweenness act as bridges connecting different parts of the network.

Usage

centrality_betweenness(x, ...)

Arguments

Value

Named numeric vector of betweenness values.

See Also

centrality for computing multiple measures at once, centrality_load for a related measure.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_betweenness(adj)

Description

Number of shortest path trees where the node appears in more than n/4 paths.

Usage

centrality_bottleneck(x, mode = "all", ...)

Arguments

Value

Named integer vector of bottleneck centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_bottleneck(adj)

Description

Product of betweenness and bridging coefficient. Identifies nodes that bridge communities.

Usage

centrality_bridging(x, ...)

Arguments

Value

Named numeric vector of bridging centrality values.

See Also

centrality for computing multiple measures at once, centrality_local_bridging for the local variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_bridging(adj)

Description

Coordinator brokerage (w_I): count of open directed 2-paths $A \to V \to A$ passing through node $V$, where all three nodes belong to $V$'s group. The broker mediates contact between two in-group members.

Usage

centrality_brokerage_coordinator(x, membership = NULL, ...)

Arguments

Details

Bit-exact match against sna::brokerage$raw.nli[, "w_I"]. Counts OPEN 2-paths only — those where no direct edge from a to c exists. Directed-only; returns NA with a warning on undirected input.

Value

Named integer vector of coordinator role counts.

References

Gould, R. V., & Fernandez, R. M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology, 19, 89-126.

See Also

centrality, centrality_brokerage_itinerant, centrality_brokerage_representative, centrality_brokerage_gatekeeper, centrality_brokerage_liaison.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_coordinator(adj, membership = c(1, 1, 2, 2))

Description

Gatekeeper brokerage (b_OI): count of open directed 2-paths $A \to V \to B$ where $V$ and $B$ are in the same group and $A$ is in a different group. The broker acts as a gate letting in-group members receive contact from outside.

Usage

centrality_brokerage_gatekeeper(x, membership = NULL, ...)

Arguments

Details

Bit-exact match against sna::brokerage$raw.nli[, "b_OI"]. Directed-only.

Value

Named integer vector of gatekeeper role counts.

References

Gould & Fernandez (1989).

See Also

centrality_brokerage_coordinator.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_gatekeeper(adj, membership = c(1, 1, 2, 2))

Description

Itinerant brokerage (w_O): count of open directed 2-paths $A \to V \to A$ where the two endpoints are in the same group but the broker $V$ is in a different group. The broker mediates within another group as an outsider.

Usage

centrality_brokerage_itinerant(x, membership = NULL, ...)

Arguments

Details

Bit-exact match against sna::brokerage$raw.nli[, "w_O"]. Directed-only.

Value

Named integer vector of itinerant role counts.

References

Gould & Fernandez (1989).

See Also

centrality_brokerage_coordinator.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_itinerant(adj, membership = c(1, 1, 2, 2))

Description

Liaison brokerage (b_O): count of open directed 2-paths $A \to V \to B$ where all three nodes belong to different groups. The broker mediates between two groups to neither of which they belong.

Usage

centrality_brokerage_liaison(x, membership = NULL, ...)

Arguments

Details

Bit-exact match against sna::brokerage$raw.nli[, "b_O"]. Directed-only.

Value

Named integer vector of liaison role counts.

References

Gould & Fernandez (1989).

See Also

centrality_brokerage_coordinator.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_liaison(adj, membership = c(1, 1, 2, 2))

Description

Representative brokerage (b_IO): count of open directed 2-paths $A \to V \to B$ where $A$ and $V$ are in the same group and $B$ is in a different group. The broker represents their group outward.

Usage

centrality_brokerage_representative(x, membership = NULL, ...)

Arguments

Details

Bit-exact match against sna::brokerage$raw.nli[, "b_IO"]. Directed-only.

Value

Named integer vector of representative role counts.

References

Gould & Fernandez (1989).

See Also

centrality_brokerage_coordinator.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_representative(adj, membership = c(1, 1, 2, 2))

Description

Minimum difference between own and competitor's closer-node count. Measures how much a node is at the center of the graph.

Usage

centrality_centroid(x, mode = "all", ...)

Arguments

Value

Named numeric vector of centroid values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_centroid(adj)

Description

Inverse of the average shortest path distance from a node to all others. For directed networks, centrality_incloseness and centrality_outcloseness measure incoming and outgoing closeness.

Usage

centrality_closeness(x, mode = "all", ...)

centrality_incloseness(x, ...)

centrality_outcloseness(x, ...)

Arguments

Value

Named numeric vector of closeness values.

See Also

centrality for computing multiple measures at once, centrality_harmonic for a variant that handles disconnected graphs.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_closeness(adj)

Description

Drop in the Wiener index when a node is removed. Higher values indicate more critical nodes for overall connectivity.

Usage

centrality_closeness_vitality(x, mode = "all", ...)

Arguments

Value

Named numeric vector of closeness vitality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_closeness_vitality(adj)

Description

Product of clustering coefficient and sum of (neighbor degree + 1).

Usage

centrality_clusterrank(x, mode = "all", ...)

Arguments

Value

Named numeric vector of ClusterRank values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_clusterrank(adj)

Description

Total communicability: row sums of the matrix exponential of the adjacency matrix. Measures a node's ability to broadcast information through all paths.

Usage

centrality_communicability(x, ...)

Arguments

Value

Named numeric vector of communicability values.

See Also

centrality for computing multiple measures at once, centrality_subgraph for the diagonal-only variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_communicability(adj)

Description

Fraction of total communicability that passes through each node.

Usage

centrality_communicability_betweenness(x, ...)

Arguments

Value

Named numeric vector of communicability betweenness values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_communicability_betweenness(adj)

Description

Network constraint measuring the extent to which a node's connections are redundant. Low constraint indicates access to structural holes (brokerage opportunities).

Usage

centrality_constraint(x, ...)

Arguments

Value

Named numeric vector of constraint values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_constraint(adj)

Description

Assigns each node to its maximum k-core. A k-core is a maximal subgraph where every node has at least k connections within the subgraph.

Usage

centrality_coreness(x, mode = "all", ...)

Arguments

Value

Named numeric vector of coreness values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_coreness(adj)

Description

Count of all cliques (not just maximal) containing each node. Measures embeddedness in dense substructures.

Usage

centrality_cross_clique(x, ...)

Arguments

Value

Named integer vector of cross-clique counts.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_cross_clique(adj)

Description

Betweenness based on electrical current flow rather than shortest paths. Uses the Laplacian pseudoinverse. Requires a connected graph.

Usage

centrality_current_flow_betweenness(x, ...)

Arguments

Value

Named numeric vector of current flow betweenness values.

See Also

centrality for computing multiple measures at once, centrality_betweenness for the shortest-path variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_current_flow_betweenness(adj)

Description

Information centrality based on electrical current flow through the network. Uses the pseudoinverse of the Laplacian matrix. Requires a connected graph.

Usage

centrality_current_flow_closeness(x, ...)

Arguments

Value

Named numeric vector of current flow closeness values.

See Also

centrality for computing multiple measures at once, centrality_closeness for the shortest-path variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_current_flow_closeness(adj)

Description

Alias for residual closeness centrality: sum of 1/2^d.

Usage

centrality_dangalchev(x, mode = "all", ...)

Arguments

Value

Named numeric vector of Dangalchev closeness values.

See Also

centrality for computing multiple measures at once, centrality_residual_closeness (equivalent).

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_dangalchev(adj)

Description

Sum of delta^d over all nodes, where d is the shortest path distance. Nodes near many others get higher scores. The decay_parameter controls the distance penalty.

Usage

centrality_decay(x, mode = "all", decay_parameter = 0.5, ...)

Arguments

Value

Named numeric vector of decay centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_decay(adj, decay_parameter = 0.5)

Description

Number of edges connected to each node. For directed networks, centrality_indegree counts incoming edges and centrality_outdegree counts outgoing edges.

Usage

centrality_degree(x, mode = "all", ...)

centrality_indegree(x, ...)

centrality_outdegree(x, ...)

Arguments

Value

Named numeric vector of degree values.

See Also

centrality for computing multiple measures at once, centrality_strength for the weighted version.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_degree(adj)

Description

Sum of scaled degrees of a node and its neighbors, measuring the node's potential for spreading information through the network.

Usage

centrality_diffusion(x, mode = "all", lambda = 1, ...)

Arguments

Details

Two methods are supported. "kandhway_kuri" (Kandhway & Kuri, 2014) computes the 1-hop binary-degree neighborhood sum and is the default for raw matrices, igraph objects, and other non-tna inputs. "power_series" computes $\mathrm{rowSums}(P + P^2 + \ldots + P^n)$ on the weighted matrix (with diag(P) := 0 when loops = FALSE) and matches tna::centralities(., measures = "Diffusion") byte-for-byte. For tna inputs, the default switches to "power_series" to match user expectation; pass diffusion_method = "kandhway_kuri" to force the binary-degree formula.

Value

Named numeric vector of diffusion centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_diffusion(adj)

Description

Shannon entropy of the edge weight distribution per node. Measures how evenly a node distributes its connections.

Usage

centrality_diversity(x, ...)

Arguments

Value

Named numeric vector of diversity centrality values.

See Also

centrality for computing multiple measures at once.

Examples

mat <- matrix(c(0, .5, .3, .5, 0, .8, .3, .8, 0), 3, 3)
rownames(mat) <- colnames(mat) <- c("A", "B", "C")
centrality_diversity(mat)

Description

Edge count divided by max component size^1.5 in the neighborhood subgraph.

Usage

centrality_dmnc(x, mode = "all", dmnc_epsilon = 1.7, ...)

Arguments

Value

Named numeric vector of DMNC values.

See Also

centrality for computing multiple measures at once, centrality_mnc for the size-only variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_dmnc(adj)

Description

Maximum shortest path distance from a node to any other node. For directed networks, centrality_ineccentricity and centrality_outeccentricity use incoming and outgoing paths.

Usage

centrality_eccentricity(x, mode = "all", ...)

centrality_ineccentricity(x, ...)

centrality_outeccentricity(x, ...)

Arguments

Value

Named numeric vector of eccentricity values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_eccentricity(adj)

Description

Network effective size: degree minus redundancy. Measures non-redundant contacts in ego network.

Usage

centrality_effective_size(x, ...)

Arguments

Value

Named numeric vector of effective size values.

See Also

centrality for computing multiple measures at once, centrality_constraint for a related structural holes measure.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_effective_size(adj)

Description

Influence-based centrality where a node's score depends on the scores of its neighbors. Nodes connected to other high-scoring nodes get higher scores.

Usage

centrality_eigenvector(x, ...)

Arguments

Value

Named numeric vector of eigenvector centrality values.

See Also

centrality for computing multiple measures at once, centrality_pagerank for a random walk variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_eigenvector(adj)

Description

Graph-theoretic entropy based on shortest path distribution in the residual graph after removing the node.

Usage

centrality_entropy(x, mode = "all", ...)

Arguments

Value

Named numeric vector of entropy centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_entropy(adj)

Description

Sum of neighbor degrees. Simple but effective influence proxy.

Usage

centrality_expected(x, mode = "all", ...)

Arguments

Value

Named numeric vector of expected centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_expected(adj)

Description

Signed-weight sum of a node's edges (Robinaugh, Millner & McNally 2016). The appropriate centrality for networks with positive and negative edges (partial-correlation, glasso, signed correlation networks) where treating negative edges as positive magnitudes can be misleading.

Usage

centrality_expected_influence_1(x, mode = "out", ...)

Arguments

Value

Named numeric vector of expected-influence values (signed).

References

Robinaugh DJ, Millner AJ, McNally RJ (2016). Identifying highly influential nodes in the complicated grief network. Journal of Abnormal Psychology, 125(6), 747-757.

See Also

centrality_expected_influence_2 for the two-step variant, centrality_strength for the weighted-degree analogue.

Examples

# Signed weight matrix (partial correlations, for example)
W <- matrix(c( 0.0,  0.5, -0.3,  0.2,
               0.5,  0.0,  0.4, -0.1,
              -0.3,  0.4,  0.0,  0.6,
               0.2, -0.1,  0.6,  0.0), 4, 4, byrow = TRUE)
rownames(W) <- colnames(W) <- c("A", "B", "C", "D")
centrality_expected_influence_1(W)

Description

Two-step signed-weight sum: a node's own expected influence (EI1) plus the weighted sum of its neighbors' EI1 (Robinaugh, Millner & McNally 2016). Captures both the node's direct influence and the influence it exerts indirectly via highly-connected neighbors.

Usage

centrality_expected_influence_2(x, mode = "out", ...)

Arguments

Value

Named numeric vector of two-step expected-influence values.

References

Robinaugh DJ, Millner AJ, McNally RJ (2016). Identifying highly influential nodes in the complicated grief network. Journal of Abnormal Psychology, 125(6), 747-757.

See Also

centrality_expected_influence_1 for the one-step variant.

Examples

W <- matrix(c( 0.0,  0.5, -0.3,  0.2,
               0.5,  0.0,  0.4, -0.1,
              -0.3,  0.4,  0.0,  0.6,
               0.2, -0.1,  0.6,  0.0), 4, 4, byrow = TRUE)
rownames(W) <- colnames(W) <- c("A", "B", "C", "D")
centrality_expected_influence_2(W)

Description

Max-flow based betweenness centrality.

Usage

centrality_flow_betweenness(x, ...)

Arguments

Value

Named numeric vector of flow betweenness values.

See Also

centrality for computing multiple measures at once, centrality_betweenness for shortest-path variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_flow_betweenness(adj)

Description

Inter-community brokerage weighted by centrality. Combines participation with degree information. Requires community membership.

Usage

centrality_gateway(x, membership = NULL, mode = "all", ...)

Arguments

Value

Named numeric vector of gateway coefficient values (0-1).

See Also

centrality for computing multiple measures at once, centrality_participation for the simpler participation coefficient.

Examples

adj <- matrix(c(0,1,1,0,0, 1,0,1,0,0, 1,1,0,1,0, 0,0,1,0,1, 0,0,0,1,0), 5, 5)
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
centrality_gateway(adj, membership = c(1, 1, 1, 2, 2))

Description

Sum of alpha^d over all nodes. Generalization of decay centrality matching tidygraph's implementation.

Usage

centrality_generalized_closeness(x, mode = "all", decay_parameter = 0.5, ...)

Arguments

Value

Named numeric vector of generalized closeness values.

See Also

centrality for computing multiple measures at once, centrality_decay (equivalent formulation).

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_generalized_closeness(adj)

Description

Sum of 1/d(v,w) normalized by (n-1). Variant of closeness using harmonic mean of distances.

Usage

centrality_gilschmidt(x, mode = "all", ...)

Arguments

Value

Named numeric vector of Gil-Schmidt power index values.

See Also

centrality for computing multiple measures at once, centrality_harmonic for a related measure.

Examples

adj <- matrix(c(0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_gilschmidt(adj)

Description

Sum of 1/d^2 over all reachable node pairs. Robust to disconnected graphs.

Usage

centrality_harary(x, mode = "all", ...)

Arguments

Value

Named numeric vector of Harary centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_harary(adj)

Description

Sum of inverse shortest path distances to all other nodes. Unlike closeness, harmonic centrality handles disconnected graphs naturally (unreachable nodes contribute 0 instead of making the measure undefined).

Usage

centrality_harmonic(x, mode = "all", ...)

centrality_inharmonic(x, ...)

centrality_outharmonic(x, ...)

Arguments

Value

Named numeric vector of harmonic centrality values.

See Also

centrality for computing multiple measures at once, centrality_closeness for the traditional variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_harmonic(adj)

Description

Hubbell (1965) input-output centrality: $C = (I - w W)^{-1} \mathbf{1}$, where $W$ is the (weighted) adjacency matrix and $w$ is a weight factor that must satisfy $w \cdot \rho(W) < 1$ for the system to be solvable.

Usage

centrality_hubbell(x, hubbell_weight = 0.5, ...)

Arguments

Details

Bit-exact match against centiserve::hubbell when edge weights are passed explicitly (cograph mirrors centiserve's full-inverse LAPACK call path).

Value

Named numeric vector of Hubbell centrality values (or NA if the system is not solvable).

Note on centiserve equivalence

centiserve::hubbell(g, weights = NULL) silently resets all edge weights to 1, ignoring the graph's weight attribute. To reproduce cograph's values with centiserve on a weighted graph, pass weights = igraph::E(g)$weight explicitly.

References

Hubbell, C. H. (1965). An input-output approach to clique identification. Sociometry, 28(4), 377-399.

See Also

centrality, centrality_katz.

Examples

# Small weighted path graph; spectral radius permits weightfactor = 0.5
adj <- matrix(0, 4, 4)
adj[1,2] <- adj[2,1] <- adj[2,3] <- adj[3,2] <- adj[3,4] <- adj[4,3] <- 0.3
rownames(adj) <- colnames(adj) <- LETTERS[1:4]
centrality_hubbell(adj, hubbell_weight = 0.5)

Description

Information centrality (Stephenson & Zelen 1989) measures a node's importance in terms of the "information" contained in all paths (not only shortest) passing through it. Defined via the inverse of a Laplacian-like matrix, yielding per-node $IC_i = 1 / (C_{ii} + (\mathrm{tr}(C) - 2 R_i) / n)$ where $C = A^{-1}$ and $R_i$ is the row sum of $C$.

Usage

centrality_information(x, ...)

Arguments

Details

Bit-exact match against sna::infocent on connected undirected graphs (cograph mirrors sna's exact construction and call sequence).

Value

Named numeric vector of information centrality values.

References

Stephenson, K., & Zelen, M. (1989). Rethinking centrality: Methods and examples. Social Networks, 11(1), 1-37.

See Also

centrality, centrality_current_flow_closeness.

Examples

adj <- matrix(c(0,1,1,0, 1,0,1,1, 1,1,0,1, 0,1,1,0), 4, 4)
rownames(adj) <- colnames(adj) <- LETTERS[1:4]
centrality_information(adj)

Description

Distance-based influence: sum of 1 - (d-1)/max(d) over all nodes.

Usage

centrality_integration(x, mode = "all", ...)

Arguments

Value

Named numeric vector of integration centrality values.

See Also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_integration(adj)

Description

Katz (1953) status index: $C = (I - \alpha A^T)^{-1} \mathbf{1}$. Each node's score sums attenuated walks of every length back to it, with attenuation $\alpha$ applied per step. Rankings are identical to Bonacich's alpha centrality with a uniform exogenous vector.

Usage

centrality_katz(x, katz_alpha = 0.1, ...)

Arguments

Details

Equivalence is verified bit-exact against centiserve::katzcent (cograph mirrors centiserve's exact LAPACK call sequence) and at machine epsilon against igraph::alpha_centrality(exo = 1) and networkx.katz_centrality_numpy.

Value

Named numeric vector of Katz centrality values.

References

Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18(1), 39-43.

See Also

centrality, centrality_eigenvector, centrality_pagerank.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_katz(adj)

Description

Count of nodes reachable within shortest path distance k. Measures how many nodes a given node can reach quickly.

Usage

centrality_kreach(x, mode = "all", k = 3, ...)

Arguments