Package 'toporanga'

Extract all possible toposorts of a graph

Description

Some toporanga graphs can be topologically sorted in many ways, but arrange will generate only one, random order. This function allows to list all of them. Use sample_toposort to fairly sample a single toposort.

Usage

all_toposorts(x, ..., limit = Inf)

Arguments

x	a toporanga_graph object.
...	ignored.
limit	maximal number of permutations returned; function errors when exhausted.

Value

A list of possible orderings, in a form of vectors of agent IDs.

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Arrange agents into hierarchy

Description

Estimate agent hierarchy from a tally by assembling edges in order of decreasing weight and skipping cycle-creating ones. The effect is a directed acyclic graph that can be topologically-sorted into an agent order, though this order may not be unique depending on how well the latent hierarchy is sampled and whether it even exists.

Usage

arrange(tally)

Arguments

tally

a toporanga tally object.

Value

A toporanga_graph object, representing the established graph.

Note

The method may be stochastic if there are ties in weights.

Examples

data(EcoHAB)
arrange(tally_log(EcoHAB$winner,EcoHAB$loser))

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Extract components of a tally

Description

Decomposes the tally into stronly connected components.

Usage

components(tally)

Arguments

tally

a toporanga_tally object.

Value

A vector of component IDs for each agent, named with agent IDs. Components are integers from 1 up to the component count, which is at most the number of agents. Hence, when the tally is fully strongly connected, the result is a vector of ones.

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Cumulative epoch generator

Description

Splits the event log into cumulative epochs, i.e., starting from the start up to selected number of final points. Returns an object which has to be fed into epochs argument of toporanga function.

Usage

cumulative_epochs(n, t)

Arguments

n	number of epochs. Silently capped to the number of events, if larger.
t	optional event times, vector of a same length and order as the event log given to toporanga function. When given, epochs will be generated based on equal-time breaks not equal-event-number breaks.

Value

A special function that can be passed to the epochs argument of toporanga function.

Note

If time is not given, event log must be sorted; otherwise, epochs will not make any sense.

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Diffuse the weights over indirect links.

Description

Uses the Schulze / widest path approach to re-express indirect domination into direct one. For instance, if $A\rightarrow B$ and $B\rightarrow C$ both have weight 10, but $A\rightarrow C$ has weight 3, it is gonna be corrected to 10 by this function.

Usage

diffuse(tally, blend)

Arguments

tally	a toporanga_tally object.
blend	a numerical factor to limit the effect of diffusion; weight of indirect path is multiplied by the given factor, while direct weights are not changed. When set to 1, function behaves the same as blend was not given at all, when given 0, whole diffuse returns tally unchanged.

Value

A modified toporanga_tally object.

---

Export dominance graph into Graphviz dot format

Description

Produces a string vector with the dot code that can be used to plot dominance graph with Graphviz or transfer topology to other software.

Usage

dot(x, con, ..., reduce = TRUE)

Arguments

x	a toporanga_graph to be exported.
con	if given, code is pushed to the given connection instead of returned; this can simply be a file name.
...	ignored.
reduce	if TRUE, a transitive reduction is applied to the graph, making it retain the order topology but removing all redundant edges.

Value

Graphviz dot code of the graph, invisibly when con is given.

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Example EcoHAB data

Description

Mice dominance events recorded by the Eco-HAB system. Covers a group of 10 mice and 6575 events recorded over a span of almost 5 days, corresponding to followings in the system. Contains three columns: winner, ID of winning mouse, loser, ID of a losing mice, t time of event occurrence, in seconds since the first event.

Usage

data(EcoHAB)

Format

An object of class data.frame with 6575 rows and 3 columns.

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Convert tally weights into margin weights

Description

When we have $w(A\rightarrow B)=a$ and $w(B\rightarrow A)=b<a$, this function will change $w(A\rightarrow B)$ to $a-b$ and $w(B\rightarrow A)$ to $0$.

Usage

marginise(tally)

Arguments

tally

a toporanga_tally object in which weights are going to be converted to margins.

Value

A modified toporanga_tally object.

---

Normalise tally weights

Description

When we have $w(A\rightarrow B)=a$ and $w(B\rightarrow A)=b$, this function will normalise both to sum to 1, i.e. divide by $a+b$. This way dominance matters more than engagement in conflicts between particular agents; in particular, an agent that frequently loses in typical events but always dominate over the otherwise dominating agent will come on top with normalised weights, while remain near the bottom otherwise.

Usage

normalise(tally)

Arguments

tally

a toporanga_tally object in which weights are going to be normalised.

Value

A modified toporanga_tally object.

---

Parameters of agents from a graph

Description

Pull numerical descriptors of a toporanga graph.

Usage

parameters(g)

Arguments

g	toporanga_graph object generated from tally.

Value

A data.frame object. Each of its rows corresponds to one agent. This agent's ID is listed in the Agent column. Superiors counts the number of agents which are upstream from a given agent, while Subordinates counts those downstream. This numbers correspond to a rank when when there is only one unique toposort of the dominance graph, and provide a graceful degradation if not. In particular they do not depend on random seed or the default toposort stored in the graph object. Thus, subordinate count is a recommended outcome if a single dominance score of an agent is desired. The Order column notes the aforementioned default toposort, which can be re-sampled with the sample_toposort. Additional columns may appear depending on meta-data in the graph object, in particular epoch parameters when using epoch argument of toporanga function.

---

Switch default toposorts of a graph to a random one

Description

Some toporanga graphs can be topologically sorted in many ways, but arrange will generate only one, random order. This function allows one to switch it to an another, randomly sampled one. Use all_toposorts to calculate all possible orderings.

Usage

sample_toposort(x)

Arguments

x	a toporanga graph.

Value

The same graph, with a fairly re-sampled default order.

---

Create tally from a raw matrix

Description

Creates a toporanga_tally objects from a matrix representing counts of domination events between pairs of agents.

Usage

tally_from_matrix(x)

Arguments

x	matrix to convert. It must be square, have zero diagonal, non-negative values and identical column and row names or lack of both ("1".."n" is gonna be inferred in this case).

Value

toporanga_tally object.

Note

If in doubt, use tally_log instead of this function.

---

Create tally from an event log

Description

Collects a log of domination events into a toporanga_tally object which can be fed to other functions in the package.

Usage

tally_log(winning, opposing, weight, ..., agents)

Arguments

winning	vector of IDs of winning agents.
opposing	vector of IDs of opposing agents.
weight	optional weight of the event; set to 1 for each event if not given.
...	ignored.
agents	optional vector ofg IDs of all agents; allows for ghost agents that are in the set but are not involved in any event.

Value

A toporanga_tally object.

---

A catch-all function to access package functionality in one call

Description

The general pipeline of toporanga is to tally the domination events, optionally modify the tally by diffusing event weights and/or re-scoring reciprocal weights, arrange agents into an order represented by an acyclic graph, finally to reduce it to an order or a dominance score. This function collects all of this into a single call.

Usage

toporanga(
  winning,
  opposing,
  weight,
  ...,
  agents,
  diffuse = FALSE,
  reciprocals = c(),
  output = c("parameters", "graph", "order_sample", "subordinate_count"),
  epochs
)

Arguments

winning	vector of IDs of winning agents.
opposing	vector of IDs of opposing agents.
weight	optional weight of the event; set to 1 for each event if not given.
...	ignored.
agents	optional vector of IDs of all agents; allows for ghost agents that are in the set but are not involved in any event.
diffuse	if TRUE, weight diffusion is applied. See diffuse for more details.
reciprocals	a vector of commands applied to the tally. "keep" does nothing; "marginise" reduces weights into weight margins, see marginise, "zero" zeroes opposing weights, see zero_opposition, "normalise" normalises weights within conflicts, see normalise; "diffuse" applies diffuse, allows to manage order in which diffuse is mixed with other modifiers; cannot be mixed with diffuse=TRUE. Normally, diffuse is applied first.
output	specifies what to return from the function. "parameters" returns the some agent parameters, see parameters; "graph" a toporanga_graph object; "order_sample" an order of agents; in case multiple is possible, a single random sample; "subordinate_count" a count of subordinate agents for each agent, which can be interpreted as a dominance score.
epochs	optional driver for applying analysis on subsets of events. See cumulative_epochs and window_epochs for more information. If given, changes the output to an aggregated version of whatever was selected with output.

Value

A result of the caclulation in a form specified by the output argument, aggregated over epochs is epochs argument is given.

Examples

data(EcoHAB)
toporanga(EcoHAB$winner,EcoHAB$loser)

---

Moving window epoch generator

Description

Splits the event log into cumulative epochs, i.e., starting from the start up to selected number of final points. Returns an object which has to be fed into epochs argument of toporanga function.

Usage

window_epochs(n, window, t)

Arguments

n	number of epochs. Silently capped to the number of events, if larger. Inferred from window if missing.
window	size of the moving window; if t is given, in the units of time, otherwise in event count. Set to range/n if not given. Larger windows are just made overlapping.
t	optional event times, vector of a same length and order as the event log given to toporanga function. When given, epochs will be generated based on equal-time breaks not equal-event-number breaks.

Value

A special function that can be passed to the epochs argument of toporanga function.

Note

If time is not given, event log must be sorted; otherwise, epochs will not make any sense.

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Zero the opposing tally weights

Description

When we have $w(A\rightarrow B)=a$ and $w(B\rightarrow A)=b<a$, this function will retain $w(A\rightarrow B)=a$ and change $w(B\rightarrow A)$ into $0$.

Usage

zero_opposition(tally, quench = FALSE)

Arguments

tally	a toporanga_tally object in which opposing weights are going to be zeroed.
quench	whether to remove tied-up weights.

Value

A modified toporanga_tally object.

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