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
Editor's Notes
- #3: If one defines the ‘neighborhood’ of a node in the graph to be the set of nodes immediately connected by a link to the current node, then the 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.