PlasmoData

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PlasmoData.jl is a package for Julia designed for representing and modeling data as graphs and for building graph models that contain large amounts of data on the nodes or edges of the graph. This package also has an accompanying package PlasmoDataPlots.jl which can be used for plotting the graphs.

PlasmoData.jl is built on the abstraction called a DataGraph. The manuscript "PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphs" details the abstraction and this package.

This package is functional and can be installed as is. It is still under development, and significant changes will continue to come. If you encounter any issues or bugs, please submit them through the Github issue tracker.

To install this package, you can use

using Pkg
Pkg.add(url="https://github.com/zavalab/PlasmoData.jl")

or

pkg> add https://github.com/zavalab/PlasmoData.jl

PlasmoData.jl is designed to store data within the graph structure and to manipulate that graph based on the data. It extends the package Graphs.jl, which is a highly optimized and efficient package in Julia. PlasmoData.jl enables representing datasets (such as matrices, images, or tensors) as graphs and for performing some topological data analysis (TDA). Some of these concepts can be found in this paper.

PlasmoData.jl uses an object DataGraph (or DataDiGraph for directed graphs) to store information. These objects contain the following features:

• g: SimpleGraph (or SimpleDiGraph for directed graphs) containing the graph structure.
• nodes: A vector of nodes, where the entries of the vector are node names. These names are of type Any so that the nodes can use a variety of naming conventions (strings, symbols, tuples, etc.)
• edges: A vector of tuples, where each tuple contains two entries, where each entry relates to a node.
• node_map: A dictionary that maps the node names to their index in the nodes vector
• edge_map: A dictionary that maps the edges to their index in the edges vector.
• node_data: An object of type NodeData that includes a matrix of data, where the first dimension of the matrix corresponds to the node, and the second dimension corresponds to attributes for the nodes. Any number of attributes is allowed, and NodeData also includes attribute names and a mapping of the attribute name to the column of the data matrix.
• edge_data: An object of type EdgeData that includes a matrix of data, where the first dimension fo the matrix corresponds to the edges, and the second dimension corresponds to attributes for the edges. Any number of attributes is allowed, and EdgeData also includes attribute names and a mapping of the attribute name to the column of the data matrix.
• graph_data: An object of type GraphData that includes a vector of data whose dimension corresponds to the number of attributes for the graph. Any number of attributes is allowed, and GraphData also includes attribute names and a mapping of the attribute name to the entry in the vector.

PlasmoData.jl includes several functions for building graphs from specific data structures, including functions like matrix_to_graph, symmetric_matrix_to_graph, and tensor_graph which build specific graph structures an save data to those structures.

PlasmoData.jl also includes functions for manipulating graph structure and analyzing the resulting topology of those structures. Functions filter_nodes, filter_edges, or aggregate change the graph structure based on the arguments passed to the functions. There are also functions such as get_EC, run_EC_on_nodes, and run_EC_on_edges that get the Euler Characteristic or the Euler Characteristic Curve for a graph, and other functions such as cycle_basis, diameter, or average_degree (largely extensions of Graphs.jl) for finding other topological descriptors.

Support for DataDiGraphs is still underway. However, for DataGraph objects, all functions shown above have doc strings, which can be accessed through the REPL by first typing ? and then the function or object name.

A DataGraph can be initiated by calling

dg = DataGraph()

PlasmoData.jl also supports building a DataGraph from an adjacency matrix. The DataGraph can be changed by adding nodes or edges to the graph, as shown below. add_node! takes two arguments: the DataGraph of interest and the node name (any data type is permitted). add_edge takes three arguments, the DataGraph of interest, and the names of two nodes in the graph.

add_node!(dg, "node1")
add_node!(dg, :node2)
add_node!(dg, 3)

add_edge!(dg, "node1", :node2)
add_edge!(dg, 3, :node2)
add_edge!(dg, "node1", 3)

Data can be added to these nodes or edges by calling add_node_data! or add_edge_data! as shown below. Here, these functions take similar arguments to add_node! or add_edge!, but they also take two additional arguments, one for the weight value and one for the attribute name (must be a string). When setting a new attribute, the other nodes or edges will receive a default value of 0.

add_node_data!(dg, "node1", 1.0,   "node_weight_1")
add_node_data!(dg, :node2,  2.0, "node_weight_1")
add_node_data!(dg, 3,       3.0,   "node_weight_1")

add_edge_data!(dg, "node1", :node2,  4.0, "edge_weight_1")
add_edge_data!(dg, :node2,  3,       5.0, "edge_weight_1")
add_edge_data!(dg, 3,       "node1", 6.0, "edge_weight_1")

Note that for DataGraphs, the order of the nodes in an edge is not important, but it is important for DataDiGraphs.

There are also functions for direclty building a graph from a set of data. Examples are shown below.

random_matrix = rand(20, 20)

matrix_graph = matrix_to_graph(random_matrix, "matrix_weight")

symmetric_random_matrix = random_matrix .+ random_matrix'

symmetric_matrix_graph = symmetric_matrix_to_graph(symmetric_random_matrix, "matrix_weight")

random_tensor = rand(20, 20, 15)

tensor_graph = tensor_to_graph(random_tensor)

To see additional examples of how PlasmoData.jl can be used, please see the examples directory within this repository.