A Complex Network Methodology for Travel Demand Model Evaluation and Validation


Travel demand can be viewed as a weighted and directed graph where nodes are the origins and destinations and links represent the trips between nodes. This paper presents a network-theoretic methodology to evaluate and validate travel demand models. We apply the proposed method on three disaggregate travel demand models from Melbourne, Australia. Statistical properties of the modeled networks are compared against the observed networks over time. The new approach reveals the network structure and connectivity of the modeled trips that are not usually captured by traditional evaluation and validation methods. Results demonstrate the complexity involved in the development, evaluation, and validation of travel demand models, which calls for advanced evaluation techniques reflecting a wide range of attributes of the observed and modeled data, travelers, mobility patterns, and complex network characteristics.

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N :

Number of nodes in the network

L :

Number of edges in the network

T :

Total number of trips

δ :

Network connectivity (2 L/N2)

a ij :

Elements of the adjacency matrix

a w ij :

Elements of the weighted adjacency matrix

F i :

Flux of a given node i

k i :

Degree of a given node i

w ij :

Weight of a given edge between node i and node j

c i :

Clustering coefficient of a given node i

b i :

Betweenness centrality of a given node i

b ij :

Betweenness centrality of a given edge between node i and node j

F〉 :

Mean node flux in the network

k〉 :

Mean node degree in the network

w〉 :

Mean edge weight in the network

c〉 :

Mean clustering coefficient in the network

wc〉 :

Mean weighted clustering coefficient in the network

CV(F) :

Coefficient of variation of node flux in the network

CV(k) :

Coefficient of variation of node degree in the network

CV(w) :

Coefficient of variation of edge weight in the network

C :

Network clustering coefficient

d T :

Average shortest path

wd T :

Average weighted shortest path

φ :

Network diameter


Weighted network diameter

ξ :

Network dissimilarity


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Correspondence to Meead Saberi.

Appendix A

Appendix A

The node degree k is the number of links connected to a node in a network where aij are elements in the adjacency matrix.

$$ {k}_i=\sum \limits_j{a}_{ij} $$

The node flux F is the number of trips starting or ending at a node where wij represents the weight or the number of trips between each pair of nodes.

$$ \kern0.5em {F}_i=\sum \limits_j{w}_{ij} $$

The clustering coefficient c for node i is calculated as the number of triangles in the graph that pass through a node.

$$ {c}_i=\frac{\left( number\ of\ pairs\ of\ neighbors\ of\ i\ that\ are\ connected\right)}{\left( number\ of\ pairs\ of\ neighbors\ of\ i\right)} $$

The network clustering coefficient C is a global measure of the extent to which nodes in a network are clustered. C is calculated as a ratio of the number of triangles to the number of connected triples of nodes, expressed as:

$$ C=\frac{\left( number\ of\ triangles\right)\times 3}{\left( number\ of\ connected\ triples\right)} $$

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Saberi, M., Rashidi, T.H., Ghasri, M. et al. A Complex Network Methodology for Travel Demand Model Evaluation and Validation. Netw Spat Econ 18, 1051–1073 (2018). https://doi.org/10.1007/s11067-018-9397-y

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  • Travel demand modeling
  • Evaluation
  • Validation
  • Complex networks
  • Structure
  • Connectivity