Development of the Theory of Six Value Aggregation Paths in Network Modeling for Spatial Analyses

The dynamic development of spatial structures entails looking for new methods of spatial analysis. The aim of this article is to develop a new theory of space modeling of network structures according to six value aggregation paths: minimum and maximum value difference, minimum and maximum value decrease, and minimum and maximum value increase. The authors show how values presenting (describing) various phenomena or states in urban space can be designed as network structures. The dynamic development of spatial structures entails looking for new methods of spatial analysis. This study analyzes these networks in terms of their nature: random or scale-free. The results show that the paths of minimum and maximum value differences reveal one stage of the aggregation of those values. They generate many small network structures with a random nature. Next four value aggregation paths lead to the emergence of several levels of value aggregation and to the creation of scale-free hierarchical network structures. The models developed according to described theory present the quality of urban areas in various versions. The theory of six paths of value combination includes new measuring tools and methods which can impact quality of life and minimize costs of bad designs or space destructions. They are the proper tools for the sustainable development of urban areas.

[1]  L. Euler.  Leonhard Euler and the Koenigsberg Bridges , 1953 .

[2]  B. Johansson,et al.  Agglomeration and networks in spatial economies , 2003 .

[3]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[4]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[5]  A. Goldberg,et al.  A heuristic improvement of the Bellman-Ford algorithm , 1993 .

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[8]  William J. Cook,et al.  Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems , 2003, Math. Program..

[9]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[10]  Graham Haughton,et al.  Spatial Planning, Devolution, and New Planning Spaces , 2010 .

[11]  Albert-Laszlo Barabasi,et al.  Deterministic scale-free networks , 2001 .

[12]  Luis M. de Campos,et al.  Searching for Bayesian Network Structures in the Space of Restricted Acyclic Partially Directed Graphs , 2011, J. Artif. Intell. Res..

[13]  Alexei Vázquez,et al.  Exact results for the Barabási model of human dynamics. , 2005, Physical review letters.

[14]  Funabashi,et al.  Scale-free network of earthquakes , 2002 .

[15]  Katarzyna Kocur-Bera,et al.  Scale-free network theory in studying the structure of the road network in Poland , 2014 .

[16]  Andrzej Biłozor,et al.  Theory of Scale-Free Networks as a New Tool in Researching the Structure and Optimization of Spatial Planning , 2018, Journal of Urban Planning and Development.

[17]  Nicholas C. Wormald,et al.  The asymptotic connectivity of labelled regular graphs , 1981, J. Comb. Theory B.

[18]  Tao Zhou,et al.  Traffic dynamics based on local routing protocol on a scale-free network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Edward A. Bender,et al.  The Asymptotic Number of Labeled Graphs with Given Degree Sequences , 1978, J. Comb. Theory A.

[20]  A. Kowalczyk.  The Use of Scale-Free Networks Theory in Modeling Landscape Aesthetic Value Networks in Urban Areas , 2015 .

[21]  H. Renssen,et al.  A global river routing network for use in hydrological modeling , 2000 .

[22]  Francis T. Durso,et al.  Network Structures in Proximity Data , 1989 .

[23]  M. Bednarczyk.  Identification of pseudo-nodal points on the basis precise leveling campaigns data and GNSS , 2017 .