supergraph visualization
DESCRIPTION
Jose Rodrigues, Agma J M Traina, Christos Faloutsos, Caetano Traina Jr (2006) SuperGraph Visualization In: 8th IEEE International Symposium on Multimedia 227-234 IEEE Press. @inproceedings { DBLP:conf/ism/RodriguesTFT06, title = "SuperGraph Visualization", year = "2006", author = "Jose Rodrigues and Agma J M Traina and Christos Faloutsos and Caetano Traina Jr", booktitle = "8th IEEE International Symposium on Multimedia", pages = "227-234", publisher = "IEEE Press", doi = "10.1109/ISM.2006.143", url = "http://www.icmc.usp.br/~junio/PublishedPapers/RodriguesJr_et_al-ISM2006.pdf", urllink = "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4061172", abstract = "Given a large social or computer network, how can we visualize it, find patterns, outliers, communities? Although several graph visualization tools exist, they cannot handle large graphs with hundred thousand nodes and possibly million edges. Such graphs bring two challenges: interactive visualization demands prohibitive processing power and, even if we could interactively update the visualization, the user would be overwhelmed by the excessive number of graphical items. To cope with this problem, we propose a formal innovation on the use of graph hierarchies that leads to GMine system. GMine promotes scalability using a hierarchy of graph partitions, promotes concomitant presentation for the graph hierarchy and for the original graph, and extends analytical possibilities with the integration of the graph partitions in an interactive environment.", keywords = "Application software , Bipartite graph , Computer networks , Computer science , Data structures , Scalability , Technological innovation , Tree graphs , Visualization , Web pages"}TRANSCRIPT
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SuperGraph Visualization
José F. Rodrigues Jr., Agma J. M. Traina, Caetano Traina Jr.
University of São PauloComputer Science Department
ICMC-USPBrazil
Christos Faloutsos
Carnegie Mellon UniversityComputer Science Department
USA
http://www.icmc.usp.br/~junio/PublishedPapers/RodriguesJr_et_al-ISM2006.pdf
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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Problem• Large graphs
– Hundred-thousand nodes or more– Million edges magnitude– web graphs, computer communication graphs ,
recommendation systems, whotrusts-whom networks, bipartite graphs of web-logs
• Visual exploration limits– Prohibitive processing power requirements for
interactive visualization– Excessive number of graphical items in screen
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Problem• Large graphs
– Hundred-thousand nodes or more– Million edges magnitude– web graphs, computer communication graphs ,
recommendation systems, whotrusts-whom networks, bipartite graphs of web-logs
• Visual exploration limits– Prohibitive processing power requirements for
interactive visualization– Excessive number of graphical items in screen
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Current Line of Research
• Draw graph according to the modular decomposition theory
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Current Line of Research
• Draw graph according to the modular decomposition theory
Limitation
Graphs represented like this are limited:- What is the relation between a given group of nodesand another group of nodes?- How many edges connect these two groups?- Which are they?- Which are the graph nodes from other groups that connect to a graph node of interest?
The graph hierarchy is dead and the original is graph is lost.
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Extending the idea
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?Graph nodesconnectivity
SuperNodesconnectivity
SuperEdges
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Extending the idea
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?Graph nodesconnectivity
SuperNodesconnectivity
SuperEdges
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Principle
• Utilize compartmented processing and presentation
• Utilize a structured partitioned version of the graph to be analized
• Add interaction for a richer experience
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Principle
• Utilize compartmented processing and presentation
• Utilize a structured partitioned version of the graph to be analized
• Add interaction for a richer experience
Our proposal
Introduce a theory and a data structure to allow the use of the hierarchical graph partition representation without loosing the original graph information.
Do this on the context of visualization, interaction and scalability
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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SuperGraphs and the Graph-Tree
• Given a graph G={V,E} a SuperGrap is a recursive partitioning of G
• A GraphTree is a SuperGraph structured as a tree
• Graph nodes are kept at the leaf nodes of the tree
• Graph edges are distributed along the tree structure
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Example
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Example
SuperNodes
GraphTreeSuperGraph
LeafSuperNodes
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Building a Graph-Tree
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Open
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Open
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Open
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Open
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Open
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Open
Open
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Open
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Open
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Open
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Open
1
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Open
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Open
Open
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Graph-Tree – LeafSuperNode
id file parent id nodes
open nodes SuperEdges
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Graph-Tree - SuperNode
id parent id
open nodes SuperEdges
sons
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Graph-Tree• A tree of graph partitions or a hierarchical
partitioning of a graph
• A new data structure for graphs
• Benefits: novel graph storage + structured graph partitions
• Provides: on demand processing/presentation + inter partitions edges information + spatial search tree (natural R-Tree properties)
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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Graph Nodes Connectivity• Theorem: if a graph node v is an open node for a
SuperNode V, then its set of parent (Parents(V)) embody all the SuperEdges that hold edges connected to v.
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Open
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Open
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Open
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Open
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Open
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Open
Open
(2,3)(2,4)
(1,5)(1,7)(4,7)
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Graph Nodes Connectivity• Theorem: if a graph node v is an open node for a
SuperNode V, then its set of parent (Parents(V)) embody all the SuperEdges that hold edges connected to v.
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Open
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Open
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Open
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Open
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Open
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Open
Open
(2,3)(2,4)
(1,5)(1,7)(4,7)
SuperNode V = FindParentOf(v);
While(v in OpenNodes(V)){
V = Parent(V);
Scan SuperEdges of V;
}
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SuperNodes Connectivity• Connectivity: the set of edges (SuperEdge)
between two SuperNodes
• Connectivity between siblings: part of the tree
• Connectivity between non-siblings: use open nodes information
• Important for SuperNode-to-SuperNode analysis
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All possible edges
• The open nodes information specifies all the nodes of a given SuperNode that connect to nodes from other SuperNodes
• Theorem: given two SuperNodes vi and vj, the Cartesian product OpenNodes(vi) x OpenNodes(vj) determines the set of all possible edges between SuperNodes vi and vj.
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Actual connecting edges• Theorem: the set of edges that actually connect any two SuperNodes vi and vj in a Graph-Tree is a subset of the unique SuperEdge ekl є FirstCommonParent(vi,vj).
vi
vj
(12,4) (16,7)
(4,12) (7,16)
(12,4) (16,7)
(4,12) (7,16)
x
vk vl
ekl={(4,12), (7,16),...}
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SuperNodes Connectivity
All possible edges
Actual connecting edges
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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Performance
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Performance
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Short Demonstration
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OutlineProblem and PrincipleSuperGraphs and the Graph-TreeConnectivityPerformanceConclusions
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Conclusion
• A new data structure for graphs– hierarchical management of graph partitions
(SuperNodes)– the original graph information is not lost– relationship (SuperEdges) between groups of nodes
instead of nodes only– scalability for visualization and interaction
• GMine - A new graph visualization tool
More at http://www.cs.cmu.edu/~junio
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End