Create a JSON, GeoJSON or shapefile for QGIS, from a list of edges and a list of nodes

Question

I have a graph composed of nodes and edges (this is in Matlab just to show something, but it can be done with other languages!)

s = [1 1 2 2 2 3 3 3];
t = [2 3 3 4 5 6 7 5];
x = [0 0 1 0 4 3 1];
y = [0 1 0 4 5 0 -1];
G = graph(s,t);
G.Nodes.X = x'; G.Nodes.Y = y';
plot(G,'XData',G.Nodes.X,'YData',G.Nodes.Y)

Just to be more clear, see here below the lists of edges and nodes:

>> G.Edges

ans =

  8×1 table

    EndNodes
    ________

     1    2 
     1    3 
     2    3 
     2    4 
     2    5 
     3    5 
     3    6 
     3    7 

>> G.Nodes

ans =

  7×2 table

    X    Y 
    _    __

    0     0
    0     1
    1     0
    0     4
    4     5
    3     0
    1    -1

Now my question:

How can transform these two lists of edges and nodes into a JSON or GeoJSON or shapefile, that can be read by QGIS?

I would like to see the same graph I have plotted here inside QGIS.

@Mayo: Your solution just shows one edge in my machine:

Answer 1

Try this in the QGIS python console

s_list = [1, 1, 2, 2, 2, 3, 3, 3]
t_list = [2, 3, 3, 4, 5, 6, 7, 5]
x_list = [0, 0, 1, 0, 4, 3, 1]
y_list = [0, 1, 0, 4, 5, 0, -1]
coords = list(zip(x_list, y_list)) # generate a list of lists containing x and y coordinates of every vertex
layer = QgsVectorLayer('LineString?crs=EPSG:4326', 'Layer', 'memory')
layer.startEditing()
for s, e in zip(s_list, t_list): # loop trow a lists of lists containing the start and end vertex index in the coords list 
    feature = QgsFeature()
    start = QgsPointXY(*coords[s - 1]) # start point 
    end =  QgsPointXY(*coords[e - 1]) # end point
    feature.setGeometry(QgsGeometry().fromPolylineXY([start, end])) # set the geometry to a QgsFeature object
    layer.addFeature(feature) # add feature to the layer
    
layer.commitChanges()
QgsProject.instance().addMapLayer(layer)

To save this vector to a file add:

QgsVectorFileWriter.writeAsVectorFormat(
    layer,
    'path/to/your/file.shp', # set here the path to your file including the file extension
    "utf-8", # file encoding
    QgsCoordinateReferenceSystem("EPSG:4326"), # set inside quotes the crs id
    "ESRI Shapefile" # set here the vector driver
    )

available vector drivers here