Graphs & Networks 2.0

Charles Pooh

Kernel Technology, R&D

Wolfram Research
(charlesp@wolfram.com)

(Row)

Outline of the talk

Overview of Graphs & Networks in Mathematica 8

Enhanced Functionality

Social Network Analysis

Network Flows

Overview of Graphs & Networks

Graphs & Network Modeling [web]

Graphs & Network Analysis [web]

White Paper: Portfolio Diversification [CDF] [paper]

Enhanced Functionality

Updates and Performance Improvements

∘ Parametric Graphs

∘ GraphData

∘ Random Graphs

∘ HighlightGraph [ref]

∘ Hamiltonian Cycles and Eulerian Cycles

∘ Centrality Measures

∘ Cliques [ref]

Enhanced Visualization

∘ Enhanced Automatic Graph Layout

∘ Multi-threaded Algorithms

∘ Support of PerformanceGoal

∘ Parameterizable Layouts [ref]

New Functions and Features

∘ SpatialGraphDistribution [ref] . GraphPropertyDistribution [ref] . …

∘ FindVertexCut . FindEdgeCut . EdgeConnectivity . VertexConnectivity . …

∘ WeaklyConnectedComponents . WeaklyConnectedGraphQ . …

∘ FindPostmanTour

∘ GraphHub . GraphLinkEfficiency . MeanGraphDistance . GraphDensity . …

∘ PlanarGraphQ . “PlanarLayout” . “BalloonEmbedding” . “SpectralLayout” . …

∘ CommunityGraphPlot

∘ Rendering Order for Vertices and Edges . Edge Bundling

Social Network Analysis

Social Media Data

∘ More empirical networks

∘ Social Media Data — Facebook, Twitter, Google+, LinkedIn [ref]

Centrality and Prestige Measures

∘ DegreeCentrality . ClosenessCentrality . BetweennessCentrality . EigenvectorCentrality . KatzCentrality . PageRankCentrality . HITSCentrality . StatusCentrality . RadialityCentrality

∘ Roles in Networks

Cohesive Groups and Community Detection

∘ FindClique . FindKClique . FindKClan . FindKClub . FindKPlex . LambdaComponents . LuccioSamiComponents

∘ FindGraphCommunities [ref]

Assortativity Mixing and Clustering

∘ GraphAssortativity

∘ GlobalClusteringCoefficient [ref] . MeanClusteringCoefficient . LocalClusteringCoefficient

Customer Story

∘ Wolfram|Alpha Facebook Report [][blog]

Network Flows

Maximum Flows

∘ FindMaximumFlow [ref]

∘ OptimumFlowData

Minimum Cost Flows

∘ FindMinimumCostFlow [ref]

∘ OptimumFlowData

Applications

∘ Transportation Problems

∘ Assignment Problems

∘ Optimization Problems

Conclusion

What’s new in Mathematica 9?

∘ Enhanced Functionality

∘ Social Network Analysis

∘ Network Flows

Future

∘ More, better and faster features

∘ Graph Editor

∘ Enhanced Graph Visualization for Large Graphs

Conference Talks on Graphs & Networks

∘ Social Network Analysis — Wednesday @ 11:30am

∘ Graph Visualization — Thursday @ 1:30pm

∘ Hands–On Workshop: Graphs and Networks — Thursday @ 12:30pm

∘ Using Mathematica for Graph Analysis in Genomics Research of Biological Regulatory Network — Friday @ 9:30am

∘ Attacking NP–Hard Graph Problems — Friday @ 1:00pm

∘ Network Flows, Planning and Scheduling — Friday @ 12:30pm