| find_loops_noscc {LoopDetectR} | R Documentation |
Loop detection in a matrix
Description
Given the Jacobian matrix of an ODE system or the adjacency matrix of a graph, this function determines all loops in the system up to the maximal number supplied. No decomposition into strongly connected components is performed.
Usage
find_loops_noscc(jacobian, max_num_loops = 1e+05)
Arguments
jacobian |
Square Jacobian matrix of an ODE system or the adjacency
matrix of a graph; captures interactions such that entry |
max_num_loops |
Positive numeric value indicating the maximal number
of loops that are reported. Default: |
Details
The input matrix delivers the directed interactions in the ODE
system; if entry (i,j) is non-zero it means that variable (or
node) i is regulated by variable (node) j. Johnson's
algorithm for path detections
from the igraph package (function:
all_simple_paths) is used.
No decomposition into strongly connected components is employed which
could be beneficial for smaller systems (compared to
find_loops).
The queried graph is increased stepwise leading to the output of loops
in a certain order determined by the order of occurrence in the Jacobian
matrix:
first the self-loops,
then feedback loops incorporating only the first and second species of the Jacobian,
then feedback loops incorporating the third and at most also the first and second species of the jacobian, etc.
If the maximal number of loops, max_num_loops, is reached, no warning is
issued. It is very probable that not all feedback loops of the system
have been found.
Up to which species this function searched before stopping due to
reaching the maximal allowed loop number can be inferred from the last
exported feedback loop.
Running the function multiple times with re-ordered jacobian as input
can enable detection of alternative feedback loops while limiting the
runtime and output size of single runs.
If columns of the Jacobian are named,
the identification is given by the attribute node_ids,
attr(result,"node_ids").
Value
A data.frame with three columns: loop, length, sign
containing up to max_num_loops loops of the systems defined
by matrix jacobian. Each entry in the loop column is a list of
identifiers that correspond to the indices of the variable in the
Jacobian matrix and denote
in which order the variables form the loop.
See Also
Examples
#sample Jacobian matrix of a system with 4 variables
jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1))
#find the first 5 feedback loops of the system
loop_list <- find_loops_noscc(jac_matrix,5)