# Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics

Volchenkov D, Blanchard P (2007) *Physical Review E* 75(2): 6104-6118.

Download

**No fulltext has been uploaded. References only!**

*Journal Article*|

*Original Article*|

*Published*|

*English*

No fulltext has been uploaded

Abstract

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an informationlike parameter which plays the role of an individual fingerprint of Genius loci. Global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem.

Publishing Year

ISSN

eISSN

PUB-ID

### Cite this

Volchenkov D, Blanchard P. Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*. 2007;75(2):6104-6118.Volchenkov, D., & Blanchard, P. (2007). Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*,*75*(2), 6104-6118. doi:10.1103/PhysRevE.75.026104Volchenkov, D., and Blanchard, P. (2007). Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*75, 6104-6118.Volchenkov, D., & Blanchard, P., 2007. Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*, 75(2), p 6104-6118. D. Volchenkov and P. Blanchard, “Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics”,

*Physical Review E*, vol. 75, 2007, pp. 6104-6118. Volchenkov, D., Blanchard, P.: Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics. Physical Review E. 75, 6104-6118 (2007).

Volchenkov, Dimitry, and Blanchard, Philippe. “Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics”.

*Physical Review E*75.2 (2007): 6104-6118.
This data publication is cited in the following publications:

This publication cites the following data publications:

### 1 Citation in Europe PMC

Data provided by Europe PubMed Central.

From complex structures to complex processes: percolation theory applied to the formation of a city.

Bitner A, Holyst R, Fialkowski M.,

PMID: 19905248

Bitner A, Holyst R, Fialkowski M.,

*Phys Rev E Stat Nonlin Soft Matter Phys*80(3 Pt 2), 2009PMID: 19905248

### 47 References

Data provided by Europe PubMed Central.

Spectra of complex networks.

Dorogovtsev SN, Goltsev AV, Mendes JF, Samukhin AN.,

PMID: 14683004

Dorogovtsev SN, Goltsev AV, Mendes JF, Samukhin AN.,

*Phys Rev E Stat Nonlin Soft Matter Phys*68(4 Pt 2), 2003PMID: 14683004

Topological analysis of urban street networks

Jiang,

Jiang,

*Environment and Planning B Planning and Design*31(1), 2004
Graph Laplacians, nodal domains, and hyperplane arrangements

BIYIKOLU,

BIYIKOLU,

*Linear Algebra and its Applications*390(), 2004
Efficiency and robustness in ant networks of galleries

Buhl,

Buhl,

*The European Physical Journal B*42(1), 2004
Networks and cities: an information perspective.

Rosvall M, Trusina A, Minnhagen P, Sneppen K.,

PMID: 15698238

Rosvall M, Trusina A, Minnhagen P, Sneppen K.,

*Phys. Rev. Lett.*94(2), 2005PMID: 15698238

Vulnerability and protection of infrastructure networks.

Latora V, Marchiori M.,

PMID: 15697641

Latora V, Marchiori M.,

*Phys Rev E Stat Nonlin Soft Matter Phys*71(1 Pt 2), 2005PMID: 15697641

Spatiotemporal analysis of complex signals: Theory and applications

Aubry,

Aubry,

*Journal of Statistical Physics*64(3-4), 1991
Does AS size determine degree in as topology?

Tangmunarunkit,

Tangmunarunkit,

*ACM SIGCOMM Computer Communication Review*31(5), 2001
Collisions Among Random Walks on a Graph

Coppersmith,

Coppersmith,

*SIAM Journal on Discrete Mathematics*6(3), 1993
Efficiency of informational transfer in regular and complex networks.

Vragovic I, Louis E, Diaz-Guilera A.,

PMID: 15903508

Vragovic I, Louis E, Diaz-Guilera A.,

*Phys Rev E Stat Nonlin Soft Matter Phys*71(3 Pt 2A), 2005PMID: 15903508

Subgraph centrality in complex networks.

Estrada E, Rodriguez-Velazquez JA.,

PMID: 16089598

Estrada E, Rodriguez-Velazquez JA.,

*Phys Rev E Stat Nonlin Soft Matter Phys*71(5 Pt 2), 2005PMID: 16089598

A graph theory interpretation of nodal regions

Nystuen,

Nystuen,

*Papers of the Regional Science Association*7(1), 1961
The Structure and Function of Complex Networks

Newman,

Newman,

*SIAM Review*45(2), 2003
Spectral measures of bipartivity in complex networks.

Estrada E, Rodriguez-Velazquez JA.,

PMID: 16383466

Estrada E, Rodriguez-Velazquez JA.,

*Phys Rev E Stat Nonlin Soft Matter Phys*72(4 Pt 2), 2005PMID: 16383466

The backbone of a city

Scellato,

Scellato,

*The European Physical Journal B*50(1-2), 2006
Vertex similarity in networks.

Leicht EA, Holme P, Newman ME.,

PMID: 16605411

Leicht EA, Holme P, Newman ME.,

*Phys Rev E Stat Nonlin Soft Matter Phys*73(2 Pt 2), 2006PMID: 16605411

The network analysis of urban streets: A dual approach

PORTA,

PORTA,

*Physica A Statistical Mechanics and its Applications*369(2), 2006
Centrality measures in spatial networks of urban streets.

Crucitti P, Latora V, Porta S.,

PMID: 16605616

Crucitti P, Latora V, Porta S.,

*Phys Rev E Stat Nonlin Soft Matter Phys*73(3 Pt 2), 2006PMID: 16605616

Centrality in networks of urban streets.

Crucitti P, Latora V, Porta S.,

PMID: 16599779

Crucitti P, Latora V, Porta S.,

*Chaos*16(1), 2006PMID: 16599779

Structural properties of planar graphs of urban street patterns.

Cardillo A, Scellato S, Latora V, Porta S.,

PMID: 16906914

Cardillo A, Scellato S, Latora V, Porta S.,

*Phys Rev E Stat Nonlin Soft Matter Phys*73(6 Pt 2), 2006PMID: 16906914

Classification of art into style periods; a factor-analytical approach.

Ruth JE, Kolehmainen K.,

PMID: 4141794

Ruth JE, Kolehmainen K.,

*Scand J Psychol*15(4), 1974PMID: 4141794

### Export

0 Marked Publications### Web of Science

View record in Web of Science®### Sources

PMID: 17358391

PubMed | Europe PMC