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## Topological Characteristics of the Dutch Road Infrastructure

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3939 | Emergence of scaling in random networks
- Barabási, Albert
- 1999
(Show Context)
Citation Context ...ényi random graph [11], [12], [13]. However, the growing interest in complex networks has prompted many researchers to propose other more complex models, e.g. small-world [26] and scale-free networks =-=[2]-=-. Besides the modeling, considerable attention has also been given to the problem of capturing, in quantitative terms, the underlying complex principles (see e.g. [3], [10], [27]). In fact, each compl... |

3329 |
Collective dynamics of ’small-world’ networks
- Watts, Strogatz
- 1998
(Show Context)
Citation Context ...s been modeled as the Erdős-Rényi random graph [11], [12], [13]. However, the growing interest in complex networks has prompted many researchers to propose other more complex models, e.g. small-world =-=[26]-=- and scale-free networks [2]. Besides the modeling, considerable attention has also been given to the problem of capturing, in quantitative terms, the underlying complex principles (see e.g. [3], [10]... |

3069 | On random graphs
- Erdös, Rényi
- 1959
(Show Context)
Citation Context ...the WWW, networks of food web, social acquaintances, citation between papers, as well as many others. Traditionally, the topology of a complex network has been modeled as the Erdős-Rényi random graph =-=[11]-=-, [12], [13]. However, the growing interest in complex networks has prompted many researchers to propose other more complex models, e.g. small-world [26] and scale-free networks [2]. Besides the model... |

2600 | The structure and function of complex networks,
- Newman
- 2003
(Show Context)
Citation Context ... underlying complex principles (see e.g. [3], [10], [27]). In fact, each complex network is classified by a set of distinguishing topological characteristics, which in part define its robustness [1], =-=[23]-=-. In this paper we analyze a set of generic topological characteristics for the complex networkoftheDutchroadinfrastructure.In the Netherlands, transportation is of special importance because the coun... |

2147 | Statistical mechanics of complex networks
- Albert, Barabási
- 2002
(Show Context)
Citation Context ..., the underlying complex principles (see e.g. [3], [10], [27]). In fact, each complex network is classified by a set of distinguishing topological characteristics, which in part define its robustness =-=[1]-=-, [23]. In this paper we analyze a set of generic topological characteristics for the complex networkoftheDutchroadinfrastructure.In the Netherlands, transportation is of special importance because th... |

1538 |
Spectral Graph Theory,
- Chung
- 1997
(Show Context)
Citation Context ... path length. Along with these widely considered topological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix =-=[5]-=-, [7], [8] and the Laplacian matrix [19], [20], [21], [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi ran... |

964 |
Small worlds: The Dynamics of Networks between Order and Randomness
- Watts
- 1998
(Show Context)
Citation Context ...nd scale-free networks [2]. Besides the modeling, considerable attention has also been given to the problem of capturing, in quantitative terms, the underlying complex principles (see e.g. [3], [10], =-=[27]-=-). In fact, each complex network is classified by a set of distinguishing topological characteristics, which in part define its robustness [1], [23]. In this paper we analyze a set of generic topologi... |

667 |
Algebraic connectivity of graphs,”
- Fiedler
- 1973
(Show Context)
Citation Context ...e Prim’s algorithm1 and the number of zero eigenvalues of the Laplacian matrix. In fact, the multiplicity of 0 as an eigenvalue of the Laplacian matrix is equal to the number of components of a graph =-=[15]-=-. The graph of the road infrastructure has exactly 170 components: the graph of the largest component (LC), defined as GLC =(NLC,LLC), contains NLC = 14098 nodes and LLC = 18689 links, respectively. T... |

567 |
Evolution of Networks: From Biological Nets to the Internet and WWW
- Dorogovtsev, Mendes
- 2003
(Show Context)
Citation Context ...[26] and scale-free networks [2]. Besides the modeling, considerable attention has also been given to the problem of capturing, in quantitative terms, the underlying complex principles (see e.g. [3], =-=[10]-=-, [27]). In fact, each complex network is classified by a set of distinguishing topological characteristics, which in part define its robustness [1], [23]. In this paper we analyze a set of generic to... |

227 | The Laplacian spectrum of graphs.
- Mohar
- 1991
(Show Context)
Citation Context ...pological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], [7], [8] and the Laplacian matrix [19], [20], =-=[21]-=-, [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random graph is that most of the topological characteri... |

217 |
Spectra of Graphs: Theory and Application
- Cvetkovic, Doob, et al.
- 1980
(Show Context)
Citation Context ... length. Along with these widely considered topological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], =-=[7]-=-, [8] and the Laplacian matrix [19], [20], [21], [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random g... |

154 |
Linked: the new science of networks. Perseus,
- Barabasi
- 2002
(Show Context)
Citation Context ...orld [26] and scale-free networks [2]. Besides the modeling, considerable attention has also been given to the problem of capturing, in quantitative terms, the underlying complex principles (see e.g. =-=[3]-=-, [10], [27]). In fact, each complex network is classified by a set of distinguishing topological characteristics, which in part define its robustness [1], [23]. In this paper we analyze a set of gene... |

66 |
Spectra of “Real-world” graphs: beyond the semi-circle law, cond-mat/100235
- Farkas, Derenyi, et al.
- 2001
(Show Context)
Citation Context ...e and regularity in the graph. Given that most of the nodes have degree 1 or 3, the regularity in the structure is expected. Hence, nodes with small degrees are responsible for the peak at λ = 0 [9], =-=[14]-=-. For instance, the local configurations with two and more deadend nodes produce eigenstates λ =0,where the dead-end node is a node with degree 1. The corresponding eigenvectors have non-zero componen... |

31 |
Spectra of complex networks
- Dorogovtsev, Goltsev, et al.
(Show Context)
Citation Context ...ucture and regularity in the graph. Given that most of the nodes have degree 1 or 3, the regularity in the structure is expected. Hence, nodes with small degrees are responsible for the peak at λ = 0 =-=[9]-=-, [14]. For instance, the local configurations with two and more deadend nodes produce eigenstates λ =0,where the dead-end node is a node with degree 1. The corresponding eigenvectors have non-zero co... |

29 |
Performance Analysis of Communications Networks and Systems
- Mieghem
- 2006
(Show Context)
Citation Context ...e advantage of the Erdős-Rényi random graph is that most of the topological characteristics can be analytically expressed in contrast to many others models where computations are hardly possible [4], =-=[25]-=-. The paper is organized as follows. Section 2 explains how the Dutch road infrastructure can be represented by a graph. Section 3 presents the analysis of the set of generic topological characteristi... |

18 | A spectral analysis of the Internet topology“,
- Vukadinović, Huang, et al.
- 2001
(Show Context)
Citation Context ...ions with two and more deadend nodes produce eigenstates λ =0,where the dead-end node is a node with degree 1. The corresponding eigenvectors have non-zero components only at the dead-end nodes [16], =-=[24]-=-. More local configurations that produce zeroeigenvalueareshowninFigure8.Infact, each time when two rows in the adjacency matrix A are the same, the rank of A decreases with 1, which is equivalent to ... |

8 | Trees with Cantor Eigenvalue Distribution
- He, Liu, et al.
- 2003
(Show Context)
Citation Context ...igurations with two and more deadend nodes produce eigenstates λ =0,where the dead-end node is a node with degree 1. The corresponding eigenvectors have non-zero components only at the dead-end nodes =-=[16]-=-, [24]. More local configurations that produce zeroeigenvalueareshowninFigure8.Infact, each time when two rows in the adjacency matrix A are the same, the rank of A decreases with 1, which is equivale... |

3 |
Leiserson, C.:Introduction to Algorithms
- Cormen, Stein, et al.
- 2001
(Show Context)
Citation Context ...set of the links that forms a tree that includes every node, where the total weight of all the links in the tree is minimized. When a graph is unweighted, any spanning tree is a minimum spanning tree =-=[6]-=-. TABLE I NUMBER OF CLUSTERS SNc WITH SIZE Nc IN THE ROAD INFRASTRUCTURE GRAPH GR. INTHE ANALYSIS OF GR, WE ALSO CONSIDER TWO SUBGRAPHS: THE GRAPH GLC OF THE LARGEST COMPONENT WITH NLC = 14098 NODES A... |

3 |
Laplacian matrices of graphs: A survey," Linear Algebra and its
- Merris
- 1994
(Show Context)
Citation Context ...onsidered topological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], [7], [8] and the Laplacian matrix =-=[19]-=-, [20], [21], [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random graph is that most of the topologica... |

1 |
I.AND TORGAŠEV, A.,Recent results in the theory of graph spectra
- CVETKOVIĆ, DOOB, et al.
- 1988
(Show Context)
Citation Context ...th. Along with these widely considered topological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], [7], =-=[8]-=- and the Laplacian matrix [19], [20], [21], [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random graph ... |

1 |
AND RÉNYI, A.,"Onthe strength of connectedness of a random graph
- ERDŐS
- 1961
(Show Context)
Citation Context ...works of food web, social acquaintances, citation between papers, as well as many others. Traditionally, the topology of a complex network has been modeled as the Erdős-Rényi random graph [11], [12], =-=[13]-=-. However, the growing interest in complex networks has prompted many researchers to propose other more complex models, e.g. small-world [26] and scale-free networks [2]. Besides the modeling, conside... |

1 |
AND PITTEL, B.,"The birth of the giant component
- JANSON, KNUTH, et al.
- 1993
(Show Context)
Citation Context ...ER] = p(NLC − 1) = log (NLC) =9.55, isratherlow.Thisisdueto 2 The value of the link probability p above which a random graph almost surely becomes connected tends, for large N, topc∼ (for details see =-=[17]-=-). log N N 2sPr[D = k] 0.7 0.6 0.5 0.4 0.3 0.2 0.1 road graph largest comp. of road graph remaining comps of road graph 0 1 2 3 4 5 6 degree k Fig. 1. The degree distribution of GR, along with GLC and... |

1 |
J.H.,"Sustainability in today’s traffic in the Netherlands
- KRAAY
- 1993
(Show Context)
Citation Context ...tion is of special importance because the country functions as a gateway for the traffic of goods between western Europe and the rest of the world. Moreover, the rapid grow in the use of private cars =-=[18]-=- motivates an analysis of the underlying structure to better understand the ongoing traffic problem. For the complex network of the road infrastructure we analyze the characteristics related to the co... |

1 |
survey of graph Laplacians", Linear and Multilinear Algebra 39
- MERRIS, A
- 1995
(Show Context)
Citation Context ...red topological characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], [7], [8] and the Laplacian matrix [19], =-=[20]-=-, [21], [22]. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random graph is that most of the topological char... |

1 |
B.,"Laplace eigenvalues of graphs: a survey", Discrete
- MOHAR
- 1992
(Show Context)
Citation Context ...cal characteristics we also consider the spectrum of the road graph, i.e. the collection of all eigenvalues of the associated adjacency matrix [5], [7], [8] and the Laplacian matrix [19], [20], [21], =-=[22]-=-. Furthermore, we compare most of the considered characteristics to those in the ErdősRényi random graph. The advantage of the Erdős-Rényi random graph is that most of the topological characteristics ... |