# An Introduction to the Network Weight Matrix

Recent working paper

Ermagun, Alireza, and Levinson, D. (2016) An Introduction to the Network Weight Matrix (

*Working Paper*).

This study introduces the network weight matrix as a replacement for the spatial weight matrix to measure the spatial dependence between links of a network. This matrix stems from the concept of betweenness centrality and vulnerability in network science. The elements of the matrix are a function not simply of proximity, but of network topology, network structure, and demand configuration. The network weight matrix has distinctive characteristic, which are capable of reflecting spatial dependence between traffic links: (1) The elements are allowed to have negative and positive values, which capture competitive and complementary nature of links, (2) The diagonal elements are not fixed to zero, which takes the self-dependence of a link upon itself into consideration, and (3) The elements not only reflect the spatial dependence based on the network structure, but they acknowledge the demand configuration as well. We verified the network weight matrix by modeling traffic flows in a 3x3 grid test network with 9 nodes and 24 directed links connecting 72 origin-destination (OD) pairs. The results disclose models encompassing the network weight matrix outperform both models without spatial components and models with the spatial weight matrix. This leads inexorably to the conclusion that the network weight matrix represents a more accurate and defensible spatial dependency between traffic links, and thereby augments traffic flow prediction.