MatrixNetworks
This package consists of a collection of network algorithms. In short, the major difference between MatrixNetworks.jl and packages like LightGraphs.jl or Graphs.jl is the way graphs are treated.
In Graphs.jl, graphs are created through Graph()
and DiGraph()
which are based on the representation of
MatrixNetworks is based on the philosophy that there should be no distinction between a matrix and a network  thus the name.
For example, d,dt,p = bfs(A,1)
computes the bfs distance from the node represented by row 1 to all other nodes of the graph with adjacency matrix A. (A can be of type SparseMatrixCSC
or MatrixNetwork
). This representation can be easier to work with and handle.
The package provides documentation with sample runs for all functions  viewable through Julia’s REPL. These sample runs come with sample data, which makes it easier for users to get started on MatrixNetworks
.
Package Installation:
To install package
using Pkg
Pkg.add("MatrixNetworks")
using MatrixNetworks
Example
?bfs
?bipartite_matching
To run test cases:
Pkg.test("MatrixNetworks")
Data available:
For a full list of all datasets:
matrix_network_datasets()
Loading data example:
load_matrix_network("clique10")
Some examples:
largest_component
: Return the largest connected component of a graph

Acc
is a sparse matrix containing the largest connected piece of a directed graphA

p
is a logical vector indicating which vertices inA
were chosen
A = load_matrix_network("dfs_example")
Acc,p = largest_component(A)
clustercoeffs
: Compute undirected clustering coefficients for a graph

cc
is the clustering coefficients
A = load_matrix_network("clique10")
cc = clustercoeffs(MatrixNetwork(A))
bfs
: Compute breadth first search distances starting from a node in a graph

d
is a vector containing the distances of all nodes from nodeu
(1
in the example below) 
dt
is a vector containing the discover times of all the nodes 
pred
is a vector containing the predecessors of each of the nodes
A = load_matrix_network("bfs_example")
d,dt,pred = bfs(A,1)
scomponents
: Compute the strongly connected components of a graph
A = load_matrix_network("cores_example")
sc = scomponents(A)
sc.number #number of connected componenets
sc.sizes #sizes of components
sc.map #the mapping of the graph nodes to their respective connected component
strong_components_map(A) # if you just want the map
sc_enrich = enrich(sc) # produce additional enriched output includes:
sc_enrich.reduction_matrix
sc_enrich.transitive_map
sc_enrich.transitive_order
Can work on ei
,ej
:
ei = [1;2;3]
ej = [2;4;1]
scomponents(ei,ej)
bipartite_matching
: Return a maximum weight bipartite matching of a graph
ei = [1;2;3]
ej = [3;2;4]
BM = bipartite_matching([10;12;13],ei,ej)
BM.weight
BM.cardinality
BM.match
create_sparse(BM) # get the sparse matrix
edge_list(BM) # get the edgelist
edge_indicator(BM,ei,ej) # get edge indicators