Clustering coefficient

1. Clustering Coefficient
• Attribute of the visibility graph
• Simple measure of a graph
• First proposed by Watts and Strogatz
to measure ‘small world’ social
networks
Fig 1. Characteristic path length L(p) and
clustering coefficient C(p) for the family of
randomly rewired graphs

2. • Clustering coefficient is the number of links between all members of the
neighborhood divided by the total number of links that could possibly exist
given that number of nodes.
n_i denotes the number of links connecting the k_i neighbors
of node i

3. • In a visibility graph it gives an idea of how much visual information is lost when
one moves away from a specific location to any neighboring location.
Fig 2. Clustering coefficient values
for a simple configuration
Fig 3. The clustering coefficient is increased when many
points within the isovist are mutually visible.

4. Fig 4. The clustering coefficient measured for Aalto's Villa Mairea. The two floors have
been linked via the stairwells.

5. • Humans are probably well able to
recognize junctions.
• They search for promising junctions
when seeking out new parts of an
environment.
• An agent that searches out junctions is
likely to resemble a human moving
around a layout in exploratory mode.
Fig 5. The Process of Wayfinding

6. • Clustering coefficient eliminates the
need for the agent to have a highly
developed cognitive map of an
environment.
• All the agent has to do is be able to
recognize junctions
Fig 6. (a) Clustering coefficient values for a simplified Mies van der Rohe's Farnsworth House
(b) Clustering coefficient values for the building furnished and analyzed for permeability.

7. • Clustering coefficient is one measure
of a visibility graph
• Many other metrics may be used to
determine junctioness
• The way that real humans actually way
find is associated with either clustering
coefficients or with the visibility graph.
• Rule must produces agent behavior
that is similar to real observed human
movement patterns.
Fig 7. Using the visibility graph to select
possible locations for a next target destination