## Abstract

Since visibility graph analysis (VGA) was first developed (Turner and Penn 1999; Turner 2001; Turner et al., 2001) by applying traditional space syntax integration calculations to networks of overlapping isovists (or ‘making isovists syntactic’), VGA analysis has endured as a fundamental pillar of the spatial analysis toolkit. Whilst some innovations have recently taken place at the level of the isovists-grid layout (Conroy Dalton et al., 2022) the fundamental, underlying calculations of isovist-integration values have remained unchanged for over two decades.

This is quite unlike networks formed out of some of the other fundamental spatial units of analysis also featuring in space syntax analysis, namely axial lines and road segments, where improvements to the underlying algorithms have ushered in a discernible shift towards more nuanced, fractional (Dalton 2001), or weighted analytical approaches, where the angular metric (Turner 2000; Turner 2001) is conventionally employed for weight assignment.

Presently, VGA analysis dutifully adheres to the binary Boolean connections characterizing isovists: two isovists are either connected, or they are not connected, there is nothing in between.

This paper embarks on a critical inquiry, poised to challenge this prevailing paradigm and introduces a novel, weighted methodology wherein isovist analysis is enhanced with a nuanced consideration of spatial overlap. In this model two isovists can either be disconnected or, if connected, can have an infinite number of possible weightings applied to the edges of the resultant isovist-network. We are primarily considering isovists which are co-visible, i.e., they can see each other’s root, rather than those that just have any amount of overlap, i.e., are co-incident.

The weighting calculation of a is performed by making the weighting reflect the degree of overlap between two isovists. A large degree of overlap of any two isovist-polygons results in a high edge-weighting and, conversely, a small degree of overlap of any two isovist-polygons results in a low edge-weighting. These weighting, as applied to networks of isovists, can be considered directly analogous to the weights applied to axial or segmental-based graphs weighted by the degree of angular connection of the lines.

In fact, with weighting isovist-grids in this way, interesting new phenomenon are introduced, which are explored and discussed in a paper. For example, there are inherent asymmetries in the resultant weighted-isovist graphs. Isovist A may share 80% of its area with isovist B and yet isovist B may only share 40% of its area with isovist A. The implications and potentialities of this is discussed and explored.

Finally, the paper applies this new weighted isovist measure (currently termed ‘differentiated isovists’) to some example case studies, both at the building level and the urban level. Substantiating evidence is then marshalled in the paper to posit that an integration analysis predicated on the measurement of overlapping isovists-areas can notably enhance the correlation with human movement (for urban-level analyses), thus aligning with antecedent findings in the domain of axial or segmental angular aalysis. If this form of integration calculation is combined with our recent work on Restricted Randomised Visibility Graph Analysis, or R-VGA (Conroy Dalton et al., 2022; Dalton et al., 2022 etc.) we suggest that it will result in a major improvement to traditional or standard VGA analysis.

This is quite unlike networks formed out of some of the other fundamental spatial units of analysis also featuring in space syntax analysis, namely axial lines and road segments, where improvements to the underlying algorithms have ushered in a discernible shift towards more nuanced, fractional (Dalton 2001), or weighted analytical approaches, where the angular metric (Turner 2000; Turner 2001) is conventionally employed for weight assignment.

Presently, VGA analysis dutifully adheres to the binary Boolean connections characterizing isovists: two isovists are either connected, or they are not connected, there is nothing in between.

This paper embarks on a critical inquiry, poised to challenge this prevailing paradigm and introduces a novel, weighted methodology wherein isovist analysis is enhanced with a nuanced consideration of spatial overlap. In this model two isovists can either be disconnected or, if connected, can have an infinite number of possible weightings applied to the edges of the resultant isovist-network. We are primarily considering isovists which are co-visible, i.e., they can see each other’s root, rather than those that just have any amount of overlap, i.e., are co-incident.

The weighting calculation of a is performed by making the weighting reflect the degree of overlap between two isovists. A large degree of overlap of any two isovist-polygons results in a high edge-weighting and, conversely, a small degree of overlap of any two isovist-polygons results in a low edge-weighting. These weighting, as applied to networks of isovists, can be considered directly analogous to the weights applied to axial or segmental-based graphs weighted by the degree of angular connection of the lines.

In fact, with weighting isovist-grids in this way, interesting new phenomenon are introduced, which are explored and discussed in a paper. For example, there are inherent asymmetries in the resultant weighted-isovist graphs. Isovist A may share 80% of its area with isovist B and yet isovist B may only share 40% of its area with isovist A. The implications and potentialities of this is discussed and explored.

Finally, the paper applies this new weighted isovist measure (currently termed ‘differentiated isovists’) to some example case studies, both at the building level and the urban level. Substantiating evidence is then marshalled in the paper to posit that an integration analysis predicated on the measurement of overlapping isovists-areas can notably enhance the correlation with human movement (for urban-level analyses), thus aligning with antecedent findings in the domain of axial or segmental angular aalysis. If this form of integration calculation is combined with our recent work on Restricted Randomised Visibility Graph Analysis, or R-VGA (Conroy Dalton et al., 2022; Dalton et al., 2022 etc.) we suggest that it will result in a major improvement to traditional or standard VGA analysis.

Original language | English |
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Title of host publication | Proceedings of 14th International Space Syntax Symposium |

Publication status | Accepted/In press - 9 Apr 2024 |

Event | 14th International Space Syntax Symposium - The University of Cyprus, Nicosia, Cyprus Duration: 24 Jun 2024 → 28 Jun 2024 Conference number: 14 https://cyprusconferences.org/14sss/ |

### Conference

Conference | 14th International Space Syntax Symposium |
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Abbreviated title | SSS |

Country/Territory | Cyprus |

City | Nicosia |

Period | 24/06/24 → 28/06/24 |

Internet address |

## Keywords

- VGA
- R-VGA
- isovists
- fractional analysis
- weighted analysis
- isovist integration
- overlapping isovists