The induced path function $J(u, v)$ of a graph consists of the set of all vertices lying on the induced paths between vertices $u$ and $v$. This function is a special instance of a transit function. The function $J$ satisfies betweenness if $w \\in J(u, v)$ implies $u \\notin J(w, v)$ and $x \\in J(u, v)$ implies $J(u, x \\subseteq J(u, v)$, and it is monotone if $x, y \\in J(u, v)$ implies $J(x, y) \\subseteq J(u, v)$. The induced path function of a connected graph satisfying the betweenness and monotone axioms are characterized by transit axioms.

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Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Changat, M., Mathew, J., & Mulder, M. (2006). The induced path function, monotonicity and betweenness (No. EI 2006-23). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from