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### Citations

1294 |
Theory of reproducing kernels
- Aronszajn
- 1950
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Citation Context ... These kernels are natural similarity measures between nodes of the graph because it can be proved that they are dot products of an embedding of the graph in a (not explicitly defined) Hilbert space (=-=Aronszajn, 1950-=-). For its simplicity, the commute time kernel, introduced in (Fouss et al., 2007), is used as a social similarity measure between two individuals. The commute time kernel computes the average time ne... |

1188 |
The detection of disease clustering and a generalized regression approach.
- Mantel
- 1967
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Citation Context ...eople. As the spatial information as well as the relations between individuals are derived from the same source (the transactions in which the individuals have been involved), a standard Mantel test (=-=Mantel, 1967-=-) is not suited to address this issue. A similar methodology, based on the adaptation of the original permutation test, is thus proposed and illustrated in that context. 1 1 Introduction Relational mo... |

663 | Graph drawing by force-directed placement
- Fruchterman, Reingold
- 1991
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Citation Context ...ions is increasing again. The network model derived from the corresponding transactions contains 2516 nodes (1099 individuals and 1417 transactions). Using a force directed algorithm as described in (=-=Fruchterman and Reingold, 1991-=-), the three bipartite graphs are displayed in Figure 1. In this figure, the transactions are colored according to their parishes and the visual effect is that the network structure seems to be someho... |

571 | A tutorial on spectral clustering - Luxburg - 2007 |

564 |
Evolution of networks: From biological nets to the Internet and WWW
- Dorogovtsev, Mendes
- 2003
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Citation Context ... metabolic pathways (biology), social relationships, computer networks or any other kind of data where the objects under study, the “entities”, are related to each others by a given type of relation (=-=Dorogovtsev and Mendes, 2003-=-; Newman et al., 2006). In the simplest case, the graph is made of N nodes (or vertices) V = {x1, . . . , xN}, each one representing an entity, and a set of edges E ⊂ V × V , 1. This work is partially... |

449 |
The Structure and Dynamics of Networks
- Newman, Barab’asi, et al.
- 2006
(Show Context)
Citation Context ... social relationships, computer networks or any other kind of data where the objects under study, the “entities”, are related to each others by a given type of relation (Dorogovtsev and Mendes, 2003; =-=Newman et al., 2006-=-). In the simplest case, the graph is made of N nodes (or vertices) V = {x1, . . . , xN}, each one representing an entity, and a set of edges E ⊂ V × V , 1. This work is partially supported by ANR Mod... |

243 | Kernels and regularization on graphs
- Smola, Kondor
- 2003
(Show Context)
Citation Context ... L = (Lij)ij where Lij = { di if i = j −Aij if i 6= j with di = ∑ j Aij and several kernels have been derived from this matrix, whose algebraic properties are strongly related to the graph structure (=-=Smola and Kondor, 2003-=-; Kondor and Lafferty, 2002). These kernels are natural similarity measures between nodes of the graph because it can be proved that they are dot products of an embedding of the graph in a (not explic... |

203 |
The interpretation of statistical maps."
- Moran
- 1948
(Show Context)
Citation Context ...escribed by the graph are somehow linked to the geographical locations of the nodes. In (Laurent and Villa-Vialaneix, 2011), this question is tackled by the use of a Join Count (JC) permutation test (=-=Moran, 1948-=-). The method is tested on a graph built from a large corpus of medieval notarial acts: the nodes of the graph are the individuals actively involved in the transactions and the edges of the graph mode... |

194 | Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation
- Fouss, Pirotte, et al.
- 2007
(Show Context)
Citation Context ...use it can be proved that they are dot products of an embedding of the graph in a (not explicitly defined) Hilbert space (Aronszajn, 1950). For its simplicity, the commute time kernel, introduced in (=-=Fouss et al., 2007-=-), is used as a social similarity measure between two individuals. The commute time kernel computes the average time needed to reach a node from another one by a random walk on the graph. It is thus e... |

176 | Diffusion kernels on graphs and other discrete structures
- Kondor, Lafferty
- 2002
(Show Context)
Citation Context ... { di if i = j −Aij if i 6= j with di = ∑ j Aij and several kernels have been derived from this matrix, whose algebraic properties are strongly related to the graph structure (Smola and Kondor, 2003; =-=Kondor and Lafferty, 2002-=-). These kernels are natural similarity measures between nodes of the graph because it can be proved that they are dot products of an embedding of the graph in a (not explicitly defined) Hilbert space... |

30 |
Batch kernel SOM and related Laplacian methods for social network analysis
- Boulet, Jouve, et al.
- 2008
(Show Context)
Citation Context ...scribed in the next section is general enough to deal with a variety of data, this article focuses on a graph built from a corpus of medieval notarial acts. This corpus has already been described in (=-=Boulet et al., 2008-=-; Rossi and Villa-Vialaneix, 2011; Rossi et al., 2012; Hautefeuille and Jouve, 2012) and the relational model on which the present paper is based is described in (Rossi et al., 2012). In short, the ne... |

10 |
N.: Représentation d’un grand réseau à partir d’une classification hiérarchique de ses sommets
- Rossi, Villa-Vialaneix
(Show Context)
Citation Context ...ection is general enough to deal with a variety of data, this article focuses on a graph built from a corpus of medieval notarial acts. This corpus has already been described in (Boulet et al., 2008; =-=Rossi and Villa-Vialaneix, 2011-=-; Rossi et al., 2012; Hautefeuille and Jouve, 2012) and the relational model on which the present paper is based is described in (Rossi et al., 2012). In short, the network intends to model a corpus o... |

3 | Using spatial indexes for labeled network analysis
- Laurent, Villa-Vialaneix
- 2011
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Citation Context ...ph are described by a spatial information. In this case, one may be interested to understand if the relations described by the graph are somehow linked to the geographical locations of the nodes. In (=-=Laurent and Villa-Vialaneix, 2011-=-), this question is tackled by the use of a Join Count (JC) permutation test (Moran, 1948). The method is tested on a graph built from a large corpus of medieval notarial acts: the nodes of the graph ... |

2 |
Defining rural elites in the 13th to 15th centuries at the crossroads of historical, archeological and mathematical approaches. Submitted to the Journal of Interdisciplinary History
- Hautefeuille, Jouve
- 2012
(Show Context)
Citation Context ...ta, this article focuses on a graph built from a corpus of medieval notarial acts. This corpus has already been described in (Boulet et al., 2008; Rossi and Villa-Vialaneix, 2011; Rossi et al., 2012; =-=Hautefeuille and Jouve, 2012-=-) and the relational model on which the present paper is based is described in (Rossi et al., 2012). In short, the network intends to model a corpus of documents preserved at the “Archives N. Villa-Vi... |

2 |
Coefficients of association and similarity based on (presence, absence): an evaluation
- Hubalek
- 1982
(Show Context)
Citation Context ...vious one. Many other similarity measures might have been defined from the adjacency matrix, simply noting that this matrix can be viewed as a matrix with individual observations of binary variables (=-=Hubalek, 1982-=-). 3.3 Geographical distances Each individual is localized by the transactions in which he is actively involved. More precisely, the contingency table between individuals and parishes, T , can be comp... |

2 |
Analyse statistique d’un réseau social de la paysannerie médiévale
- Miquel
- 2011
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Citation Context ... might also be interesting to take into account the distances between villages while evaluating the correlation between social relations and the spatial information. Such a study has been started in (=-=Miquel, 2011-=-) and is improved in this paper. In particular, a new permutation based test is introduced to overcome the fact that the spatial information and the relations between individuals come from the same so... |

2 | Hautefeuille (2012). Exploration of a large database of French notarial acts with social network methods - Rossi, Villa-Vialaneix, et al. |