%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      
                    "Graph watermarking data set"

                    Hiba Al-khafaji and Charith Abhayaratne

               Department of Electronic and Electrical Engineering
                          The University of Sheffield
                        Sheffield, S1 3JD, United Kingdom

           Email: h.alkhafaji@sheffield.ac.uk, c.abhayaratne@sheffield.ac.uk

                                 07/02/2019

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

This data set contains the graph data used for evalaution of graph watermarking algorithms. It includes
160 types of graphs and corresponding graph data (aka, graph signal) that were used in the performance evaluation in our publication "Graph Spectral Domain Blind Watermarking"  that is accepted in ICASSP 2019 conference [1].

This data set contains the following:

-Readme.txt
-Graphs Folder 

The graphs (with specified connectivity) were generated using the Toolbox for signal processing on graphs (GSPBox) which can be found in the link (https://epfl-lts2.github.io/gspbox-html/). The Toolbox for GSPBox provides the graph structure without graph signal values. This data set incorporates the graph signals, using a correlated input, such as, a natural image.
 
The dataset includes 11 types of graphs:  Sensor, Spiral, Swiss-roll, Sphere, Minnesota, Community, Cube, Torus, David-sensor- network, Air foil and Bunny.  Their data (signal) values were obtained from 5 publicly available standard test images data (http://www.hlevkin.com/TestImages/classic.htm): Lena, Barbara, Gold Hill, Baboon and Peppers to form graph signals.  A total of 160 various graphs are included in the dataset. 

The graphs are named as follows:  <graph type>_<N>_<M>.mat
- graph type = {Sensor, Spiral, Swiss-roll, Sphere, Minnesota, Community, Cube, Torus, David-sensor- network, Air foil,Bunny}
- N = Number of nodes in the graph
- M = The source data image identifier, i.e., 1=Lena, 2=Barbara, 3=Gold Hill, 4=Baboon and 5=Peppers



Each .mat file includes the graph structure G for each graph containing the following fields:
- N                    The number of graph nodes
- coords               The graph coordinates (x,y) or (x,y,z)
- A                    The adjacency matrix 
- type                 The type of graph
- signal               The graph signal

For example the structure of Torus graph is:

G = 

    coords: [10000x3 double]
      type: 'torus'
         A: [10000x10000 logical]
         N: 10000
    signal: [100x100 uint8]


Graph data can de read into MATLAB as:  load('<graph type>_<N>_<M>.mat').


An example of loading and plotting is as follows:

   load('Sensor_2500_2.mat');
   figure; 
   for i=1:G.N
       if size(G.coords,2) == 2
          scatter(G.coords(i,2),G.coords(i,1),5,G.signal(G.coords(i,1),G.coords(i,2),’filled’);
      else                
         scatter3(G.coords(i,2),G.coords(i,1),G.coords(i,3),5,G.signal(G.coords(i,1),G.coords(i,2)),'filled');
     end;
       colormap(gray);
       hold on;
   end;
   axis off; 
	


References:
[1] H. Al-khafaji and C. Abhayaratne, "Graph Spectral Domain Blind Watermarking", (To appear in) IEEE ICASSP 2019.