The Living Thing / Notebooks :

Network and graphs, theory thereof

Abstract networks[#]_ as in the bridges of Kaliningrad, graph theory and so on. the prevalence of online social networks in modern life leads us to naturally think of those, but networks provide a natural substrate for a bunch of processes, and passing backwards and forwards between linear-algebraic formalisms and graph formalisms can illuminate both.

[1]prefixed “complex” to make sure one does not accidentally get sent to a an IT operations conference and have to talk to — brrr — engineers, whilst still letting it sound like it might be difficult and worthy, and certainly more difficult, if not less ambiguous, than “graphs”.

To learn:

To not mention:

Spectral methods

Dynamic graphs

e.g. Volodymyr Miz, Kirell Benzi, Benjamin Ricaud, and Pierre Vandergheynst, Wikipedia graph mining: dynamic structure of collective memory

As a topology for other processes

It’s not just nodes and edges and possibly a probability distribution over the occurrence of each. Networks are presumably interesting because they provide a topology upon which other processes occur. And the interaction between this theory and pure driven topology is much more complex and rich. Such models include circuit diagrams, probabilistic graphical models, neural networks, contagion processes reaction networks and others.

John Baez:

Scientists and engineers use diagrams of networks in many different ways. The Azimuth Project is investigating these, using the tools of modern mathematics. You can read articles about our research here:

…You can watch 4 lectures, an overview of network theory, here:

For now, I’m interested in conductance in electrical networks, random walks on graphs and the connection betwixt them. Where can I find out more about that? And how about the connection from those to harmonic functions?

Stochastic Petri Nets

Interaction nets

What are these?

If you add in probability, are they the same as stochastic Petri nets?

Graph software


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