Prsentation PowerPoint

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SPANGEO PROJECT Multi-Level Modelling of
Geographical Networks
LIRMM Montpellier, FR Labri Bordeaux, FR UMR
ESPACE - Univ. Montpellier 3, FR CITERE, Tours,
FR
INRETS, Lille, FR MTG, Univ. Rouen, FR Univ. de
Montréal, CA Univ. de Lausanne, CH
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Who are we ?

• SPANGEO (SPAtial Networks in GEOgraphy)
• Supported by the French National Agency of
  Research (2005-2008)
• France (Montpellier, Bordeaux, Tours, Lille)
• Switzerland (Lausanne)
• Canada (Montreal)

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Visualization and analysis ofspatial networks

• Main goals are to identify
• Reticular structures of the network
• Subgroups they define
• Organizational patterns, territorial patterns
• Major actors / factors
• Inter-disciplinarity
• Geography (flows and relationship analysis,
  cartography)
• Statistics (graphs, clustering, small worlds
  approach)
• Computer science ( graph analysis, visualization)
• Final production
• Graph analysis software dedicated to spatial
  questions

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Edge strength distinguish between neighborhoods

• Dense neighborhoods
• Weak links connect distinct subgroups

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Methodology

• Organize the network into a hierarchy of
  subgroups
• Define an edge metric we call edge strength
• Edge with dense neighborhoods have greater
  strength
• Edge with a low level of neighbors are weak and
  act as a path between distinct subgroups

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Strength look at cycles of length 3 and 4
Wuv
?3(e)
Mu Mu Wuv
?4(e)
s(Mu, Wuv)
s(Mv, Wuv)
s(Mu, Mv)
s(Wuv, Wuv)
?(e) ?3(e) ?4(e)
Strength index
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Use edge strength to infer a clustering of the
graph

• Temporarily ignore edges with weaker strength

1
3
4
2
5
3
4
3
2
4
3
3
4
2
3
1 2 3 4 5
3
2
3
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Use edge strength to infer a clustering of the
graph

• Temporarily ignore edges with weaker strength

1
3
4
2
5
3
4
3
2
4
3
3
4
2
3
1 2 3 4 5
3
2
3
threshold
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Use edge strength to infer a clustering of the
graph

• Temporarily ignore edges with weaker strength

C2
C1
C3
1 2 3 4 5
C5
C4
threshold
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Which threshold to choose ?

• The one leading to the best clustering
• Optimization problem

?
Quality index
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Hierarchical organization of the network

• The procedure can be iterated to produce a
  hierarchy of clusters
• Strength of edges is recomputed at each stage
• Threshold is locally chosen for each component
• TULIP Software
• www.tulip-sofware.org
• David Auber Bordeaux

http//mappemonde.mgm.fr n3 2005
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Prospects

• Methodological
• Output of edge strength indexes
• Output of group quality index
• Compute different variants of partitionning
  indexes
• Fuzzy partitionning
• Thematical
• Multinational firms (1990, 1996, 2006) Research
  networking
• Transport timetables Commuters (oriented
  graphs)
• Diachronic data (graph evolutions)
• Comparing several graphs on the same space
  (hypergraphs)
• Theoretical
• Geographical logics (space as an actor)
• Actors logics (actors in space)

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Prospects

• From TULIP to SPANGEO
• Additional graph tools
• Geographic models
• The project is open
• Other dynamic partners are welcome

www.tulip-software.org