Create a weighted, undirected multigraph with several edges between node 1 and node 2.

G = graph([1 1 1 1 2 3],[2 2 2 3 3 4], 1:6);
G.Edges

ans=6×2 table
    EndNodes    Weight
    ________    ______

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

Simplify the multigraph into a simple graph, such that there is only one edge between node 1 and node 2. simplify keeps the first edge between those two nodes, G.Edges(1,:), and drops the others.

G = simplify(G);
G.Edges

ans=4×2 table
    EndNodes    Weight
    ________    ______

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

Use the second input of simplify to select a method that picks between multiple edges or combines multiple edges into one.

Create a weighted multigraph. In this graph, five edges occur between node 3 and node 4, but the edges have random weights. View the edges table and plot the graph for reference.

G = graph([1 2 3 3 3 3 3 3 ],[2 3 1 4 4 4 4 4],randi(10,1,8));
G.Edges

ans=8×2 table
    EndNodes    Weight
    ________    ______

     1    2        9  
     1    3        2  
     2    3       10  
     3    4       10  
     3    4        7  
     3    4        1  
     3    4        3  
     3    4        6  

plot(G,'EdgeLabel',G.Edges.Weight)

The command simplify(G) keeps the first of the repeated edges. However, you can specify a different pick/combine method with the second input.

The options for picking between multiple edges are: 'first' (default), 'last', 'min', and 'max'. Keep the repeated edge with maximum weight.

H_pick = simplify(G,'max');
plot(H_pick,'EdgeLabel',H_pick.Edges.Weight)

The options for combining multiple edges into one are: 'sum' and 'mean'. Sum repeated edges together to produce a single edge with a larger weight.

H_comb = simplify(G,'sum');
plot(H_comb,'EdgeLabel',H_comb.Edges.Weight)

Simplify a graph while preserving self-loops using the 'keepselfloops' option.

Create a multigraph with two nodes and several self-loops. Simplify the graph and preserve self-loops.

G = graph([1 1 1 1 1 1 1 2 2 2 2],[1 1 1 1 2 2 2 2 2 2 2 ]);
plot(G)
axis equal

G = simplify(G,'keepselfloops');
plot(G)
axis equal

Use the second and third outputs of simplify to get information about how many (and which) edges are combined.

Create an undirected multigraph with three nodes and four edges.

G = graph([1 1 1 2],[2 2 3 3]);
G.Edges

ans=4×1 table
    EndNodes
    ________

     1    2 
     1    2 
     1    3 
     2    3 

Simplify the graph and specify three outputs to get additional information about the combined edges.

[G,ei,ec] = simplify(G)

G = 
  graph with properties:

    Edges: [3x1 table]
    Nodes: [3x0 table]

ei = 4×1

     1
     1
     2
     3

ec = 3×1

     2
     1
     1

ei(i) is the edge in the simplified graph that represents edge i in the old graph. Since the first two edges are repeated, ei(1) = ei(2) = 1. Also, ec(1) = 2, since there are two edges in the new graph corresponding to edge 1 in the old graph.

Show how to simplify a multigraph using the 'PickVariable' and 'AggregationVariables' name-value pairs.

Create a multigraph where the nodes represent locations and the edges represent modes of transport. The edges have properties that reflect the cost and time of each mode of transportation. Preview the edges table.

G = graph([1 1 1 1 1 1 2 2 2],[2 2 2 3 3 3 3 3 3],[],{'New York', 'Boston', 'Washington D.C.'});
G.Edges.Mode = categorical([1 2 3 1 2 3 1 2 3],[1 2 3],{'Air' 'Train' 'Bus'})';
G.Edges.Cost = [400 80 40 250 100 75 325 150 100]';
G.Edges.Time = [1 7 5 1.5 10 8 1.75 11 9]';
G.Edges

ans=9×4 table
                 EndNodes                  Mode     Cost    Time
    ___________________________________    _____    ____    ____

    {'New York'}    {'Boston'         }    Air      400        1
    {'New York'}    {'Boston'         }    Train     80        7
    {'New York'}    {'Boston'         }    Bus       40        5
    {'New York'}    {'Washington D.C.'}    Air      250      1.5
    {'New York'}    {'Washington D.C.'}    Train    100       10
    {'New York'}    {'Washington D.C.'}    Bus       75        8
    {'Boston'  }    {'Washington D.C.'}    Air      325     1.75
    {'Boston'  }    {'Washington D.C.'}    Train    150       11
    {'Boston'  }    {'Washington D.C.'}    Bus      100        9

Plot the graph for reference. Label the transportation mode on each edge, make the edge line widths proportional to the time, and the color of each edge proportional to the cost.

plot(G,'EdgeLabel',cellstr(G.Edges.Mode),'LineWidth',G.Edges.Time./min(G.Edges.Time),'EdgeCData',G.Edges.Cost)
colorbar

Use the 'min' selection method and specify the value of 'PickVariable' as the 'Time' variable to find the quickest mode of transport between each set of nodes.

t = simplify(G,'min','PickVariable','Time');
plot(t,'EdgeLabel',cellstr(t.Edges.Mode))

Use the 'sum' aggregation method and specify the value of 'AggregationVariables' as 'Cost' to compute how much money is made on each connection.

c = simplify(G,'sum','AggregationVariables','Cost');
plot(c,'EdgeLabel',c.Edges.Cost)