1. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
An outline of the Indexed Stacked Blocks graph numerical representation scheme. The number line is divided into regions corresponding to the number of nodes in the model. Each region is divided into blocks corresponding to different node label sets. Finally, the edge pattern within a model determines its index number within the relevant block

2. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
The graph structure used to illustrate the model number calculations

3. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
The geometric analogy for the sequence number for an alphabet with three symbols (a) In the three-dimensional space whose axes are the ai, all the node label sets containing n nodes lie on a two-dimensional plane whose distance from the origin increases with increasing n (b) A face-on view of the n = 4 plane showing the order in which the sequence number progresses through the points in the plane

4. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
An example of the calculation of the index number for the example graph shown in Figure 3, by reading out the adjacency matrix as a binary string after ordering the nodes according to their labels

5. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
A diagrammatic representation of the two options for dealing with the node ordering issue (a) accept all orderings: a single graph structure is mapped to three numerical values (dark grey cells), but all numerical values map to a graph structure (all cells are fully shaded light or dark) (b) choose a specific ordering: a single graph structure is only mapped to one numerical value (dark grey cell), but some numerical values do not map to any graph structures (cells containing crosses)

6. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
Graph structures used in the illustrative examples (a) The graph structure used for the first illustrative example, a repeat of that shown in Figure 3 (b) The graph structure used for the second illustrative example

7. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
The graph structure generated from the numerical value in the graph language used in Fig. 7

8. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
The search tree explored by the synthesis algorithm, with a modified ISB calculation method that ignores the number of leaves when calculating the sequence number. Search paths leading to valid architectures (those that satisfy all constraints) are shown in dark red, while paths explored that lead to invalid architectures are shown in light grey

9. Date of download: 1/1/2018
Copyright © ASME. All rights reserved.
From: A Scheme for Numerical Representation of Graph Structures in Engineering Design
J. Mech. Des. 2013;136(1): doi: /
Figure Legend:
A plot of average graph distance between nodes against estimated average geometric distance from leaves to hubs, for an exponentially-spaced sample of 500 networks with up to 20 hubs and a 5000-network targeted sample around the Pareto-optimal 10-hub network