This set of functions tries to calculate a ranking of the nodes in a graph so that nodes sharing certain topological traits are in proximity in the resulting order. These functions are of great value when composing matrix layouts and arc diagrams but could concievably be used for other things as well.

node_rank_hclust(
method = "average",
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_anneal(
cool = 0.5,
tmin = 1e-04,
swap_to_inversion = 0.5,
step_multiplier = 100,
reps = 1,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_branch_bound(
weighted_gradient = FALSE,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_traveller(
method = "two_opt",
...,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_two(
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_mds(
method = "cmdscale",
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_leafsort(
method = "average",
type = "OLO",
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_visual(
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_spectral(
normalized = FALSE,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_spin_out(
step = 25,
nstart = 10,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_spin_in(
step = 5,
sigma = seq(20, 1, length.out = 10),
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_quadratic(
criterion = "2SUM",
reps = 1,
step = 2 * graph_order(),
step_multiplier = 1.1,
temp_multiplier = 0.5,
maxsteps = 50,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_genetic(
...,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

node_rank_dendser(
...,
dist = "shortest",
mode = "out",
weights = NULL,
algorithm = "automatic"
)

## Arguments

method The method to use. See Functions section for reference The algorithm to use for deriving a distance matrix from the graph. One of "shortest" (default): Use the shortest path between all nodes "euclidean": Calculate the L2 norm on the adjacency matrix of the graph "manhattan": Calculate the L1 norm on the adjacency matrix of the graph "maximum": Calculate the supremum norm on the adjacenecy matrix of the graph "canberra": Calculate a weighted manhattan distance on the adjacency matrix of the graph "binary": Calculate distance as the proportion of agreement between nodes based on the adjacency matrix of the graph or a function that takes a tbl_graph and return a dist object with a size matching the order of the graph. Which edges should be included in the distance calculation. For distance measures based on the adjacency matrix, 'out'  will use the matrix as is, 'in' will use the transpose, and 'all' will take the mean of the two. Defaults to 'out'. Ignored for undirected graphs. An edge variable to use as weight for the shortest path calculation if dist = 'shortest' The algorithm to use for the shortest path calculation if dist = 'shortest' cooling rate minimum temperature Proportion of swaps in local neighborhood search Multiplication factor for number of iterations per temperature Number of repeats with random initialisation minimize the weighted gradient measure? Defaults to FALSE Arguments passed on to other algorithms. See Functions section for reference The type of leaf reordering, either 'GW' to use the "GW" method or 'OLO' to use the "OLO" method (both in seriation) Should the normalized laplacian of the similarity matrix be used? The number iterations to run per initialisation The number of random initialisations to perform The variance around the diagonal to use for the weight matrix. Either a single number or a decreasing sequence. The criterion to minimize. Either "LS" (Linear Seriation Problem), "2SUM" (2-Sum Problem), "BAR" (Banded Anti-Robinson form), or "Inertia" (Inertia criterion) Temperature multiplication factor between 0 and 1 The upper bound of iterations

## Value

An integer vector giving the position of each node in the ranking

## Functions

• node_rank_hclust: Use hierarchical clustering to rank nodes (see stats::hclust() for allowed methods)

• node_rank_anneal: Use simulated annealing based on the "ARSA" method in seriation

• node_rank_branch_bound: Use branch and bounds strategy to minimize the gradient measure (only feasable for small graphs). Will use "BBURCG" or "BBWRCG" in seriation dependent on the weighted_gradient argument

• node_rank_traveller: Minimize hamiltonian path length using a travelling salesperson solver. See the the solve_TSP function in TSP for an overview of possible arguments

• node_rank_two: Use Rank-two ellipse seriation to rank the nodes. Uses "R2E" method in seriation

• node_rank_mds: Rank by multidimensional scaling onto one dimension. method = 'cmdscale' will use the classic scaling from stats, method = 'isoMDS' will use isoMDS from MASS, and method = 'sammon' will use sammon from MASS

• node_rank_leafsort: Minimize hamiltonian path length by reordering leafs in a hierarchical clustering. Method refers to the clustering algorithm (either 'average', 'single', 'complete', or 'ward')

• node_rank_visual: Use Prim's algorithm to find a minimum spanning tree giving the rank. Uses the "VAT" method in seriation

• node_rank_spectral: Minimize the 2-sum problem using a relaxation approach. Uses the "Spectral" or "Spectral_norm" methods in seriation depending on the value of the norm argument

• node_rank_spin_out: Sorts points into neighborhoods by pushing large distances away from the diagonal. Uses the "SPIN_STS" method in seriation

• node_rank_spin_in: Sorts points into neighborhoods by concentrating low distances around the diagonal. Uses the "SPIN_NH" method in seriation

• node_rank_quadratic: Use quadratic assignment problem formulations to minimize criterions using simulated annealing. Uses the "QAP_LS", "QAP_2SUM", "QAP_BAR", or "QAP_Inertia" methods from seriation dependant on the criterion argument

• node_rank_genetic: Optimizes different criteria based on a genetic algorithm. Uses the "GA" method from seriation. See register_GA for an overview of relevant arguments

• node_rank_dendser: Optimizes different criteria based on heuristic dendrogram seriation. Uses the "DendSer" method from seriation. See register_DendSer for an overview of relevant arguments

## Examples

graph <- create_notable('zachary') %>%
mutate(rank = node_rank_hclust())