Keller, André A. Graph theory and economic models: from small to large size applications. (English) Zbl 1291.05200 Hliněný, Petr (ed.) et al., 6th Czech-Slovak international symposium on combinatorics, graph theory, algorithms and applications, DIMATIA Center, Charles University, Prague, Czech Republic, July 10–16, 2006. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 28, 469-476 (2007). Summary: This empirical study explores the structure of macroeconomic models using major concepts and algorithms of the graph theory. Different sizes of applications with dynamic effects are considered. We will firstly examine the matching problem when assigning the equations to the variables. We’ll also propose a simple method for improving the regular circular embedding of graphs on the basis of one of the longest circuit and adequate permutations. The determination of the maximal list of edge-disjoint circuits also produces an useful insight into the structure. A typology of the interdependent variables is proposed using the all- pairs shortest paths matrix. This classification is based on both the emissions of nodes towards the rest of the directed graph and the perturbations that the rest of the graph exerts on these nodes. The computations have been done using the softwares MATHEMATICA 5.1, LINDO 6.1 and our own programs in Fortran 77L and C++.For the entire collection see [Zbl 1109.05007]. Cited in 3 Documents MSC: 05C90 Applications of graph theory 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C38 Paths and cycles 91B64 Macroeconomic theory (monetary models, models of taxation) Keywords:macroeconomic model; directed graph; strong component (SC); longest circuit; directed acyclic graph (DAG); edge-disjoint circuits; eccentricity; in-eccentricity; all-pairs shortest paths; typology Software:Mathematica; LINDO PDFBibTeX XMLCite \textit{A. A. Keller}, Electron. Notes Discrete Math. 28, 469--476 (2007; Zbl 1291.05200) Full Text: DOI References: [1] Beld, C.A. van den, A Macro Model for The Dutch Economy; Beld, C.A. van den, A Macro Model for The Dutch Economy [2] Gondran, M.; Minoux, M., Graphs and Algorithms (1984), John Wiley: John Wiley New York, N.Y. · Zbl 1117.06010 [3] Keller, A. A., Semi-reduced Forms of Econometric Models, (Ancot, J. P., Analysing the Structure of Econometric Models (1984), Martinus Nijhoff: Martinus Nijhoff The Hague), 89-113 [4] Pemmaraju, S.; Skiena, S., Combinatorics, and Graph Theory with \(Mathematica^® (2003)\), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 1067.05001 [5] Van der Giessen, A. A., Solving non-linear systems by computer; a new method, Statistica Neerlandica, 24, 1, 41-50 (1970) [6] Wolfram, S., The \(Mathematica^®\) Book (2003), Wolfram Media Inc.: Wolfram Media Inc. Champain, IL, With associated web site This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.