# 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 LightGraphs.jl, graphs are created through Graph() and DiGraph() which are based on the representation of G as G = (V,E). Our viewpoint is different.

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 Juila’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("clique-10")
```

## 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 graph A p is a logical vector indicating which vertices in A 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("clique-10")
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 node u (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
```