Beyond the Basics of Graphs & Networks

Jaebum Jung, Wolfram Research

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Evolution of Graph Functionality in Mathematica

Version 8: Integration and Performance

Modern  extensible  platform  for  graph  and  network  modeling .

General and efficient representation of graphs and networks.

Full integration of graphs and networks into Mathematica.

More than 140 symbols are added.

Version 9: Network Flow and Performance Improvements

Extensive support for network flows including maximum flow and minimum cost flows.

New and optimized random graph distributions.

Highly optimized Eulerian and Hamiltonian cycle computations.

Version 10: Further Enhancements

Framework-wide support of multigraphs.

Framework-wide support of mixed graphs.

Built-in 3D graph visualization.

Version 11: Expanding Capabilities

Efficient Hamiltonian path function.

Comprehensive support of graphs from nearest neighbors for a variety of data, including numerical, geospatial, textual, and visual.

Ready-made graphs from curated data, including ChemicalData and WolframLanguageData.

Version 12: Aesthetic Unification and Improved Usability

Updated graph visualization functions.

New predicate functions to test weighted graphs.

Automatic inheritance of properties in all graph constructors and operations.

Version 13: Computational Geometry and Topology, and Edge Tagging

Edge tagging provides a way to distinguish between multiple edges connecting the same vertices, making your graph analysis more precise.

New functions for computational topology, a critical aspect of representing complex structures.

U.S. FOOD SUPPLY CHAIN SECURITY 
BY BRADFORD BROWN , PAUL GARVEY, PH.D. , MEGAN SMITH , ERIC HARLEY , MONICA MENDOZA , JEFF HARROLD

https://www.mitre.org/news-insights/publication/us-food-supply-chain-security-network-analysis

Key Findings and Recommendations

Vulnerability of the U.S. food supply chain.

Recommendations for resilience: data sharing, systems approach, risk assessments.

National Resilience

This case study illustrates the need for a comprehensive approach.

Emphasizes the importance of food supply chain to national resilience.

Tools

The Wolfram Physics Project

https://www.wolframphysics.org/

The Wolfram Physics Project

Structureless models with remarkable complexity.

Potential relevance to known features of fundamental physics.

Empirical investigation combined with mathematical analysis.

Contribution to the quest for a complete theory of the universe.

Interdisciplinary approach.

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Software Tools

https://www.wolframcloud.com/obj/wolframphysics/Tools/guide-page

Software Tools

https://www.wolframcloud.com/obj/wolframphysics/Tools/guide-page

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Detecting Global Community Structure in a COVID-19 Activity Correlation Network by Hiroki Sayama​

https://community.wolfram.com/groups/-/m/t/3056172

Utilizing COVID-19 Data for Global Analysis

Leveraging the vast amount of COVID-19 epidemic/public health datasets.

Studying the interconnected world through data analysis.

Using the Johns Hopkins University COVID-19 dataset for this analysis.

Exploring the global community structure through correlation networks.

Focus on countries/regions with at least 100,000 cumulative positive cases.

Global Community Structure and Pandemic Analysis

Creating a correlation network based on daily change exponents.

Identifying three major global communities within the dataset.

Robust detection of communities under different settings.

Constructing a 3D ‘phase space’ for a summary trajectory of the pandemic.

Global Community structure

Graphs in the Modern World
Thursday  10 : 00  PM  CDT

Office Hour: Graphs & Networks
Friday  8 : 30  AM  CDT