SWEN90004
Modelling Complex Software Systems
Lecture Cx.10 Networks II: Networks and ABMs
Artem Polyvyanyy, Nic Geard
artem.polyvyanyy@unimelb.edu.au;
nicholas.geard@unimelb.edu.au
Semester 1, 2021
1/9
Recap
Networks can be used to represent the structure of complex systems – the pattern of interactions between their components
We can describe the structure of networks in terms of quantitive properties such as density, degree distribution, characteristic path length, clustering coefficient, etc.
A range of network models have been proposed to describe the structure of real world complex systems, including:
small world networks scale free networks
We discussed how regular 1D and 2D lattices could be used to describe the structure of interactions in 1D and 2D cellular automata.
Today we will switch focus from network structure to network dynamics.
2/9
Network dynamics
Two types of network dynamic are often considered:
the network structure may remain static, but the state of nodes changes—dynamics on networks
the network structure changes—dynamics of networks
3/9
Dynamics on networks—SIR disease model
In week 3, we explored a Cellular Automata model of disease trans- mission on a 2D grid. As a grid can be represented as a regular lattice, it is straightforward to generalise our approach to consider the spread of infection across any network.
4/9
Dynamics on networks—SIR disease model
what effect might network structure have on the dynamics of disease spread?
which nodes in a network are at greatest risk: of being infected?
of infecting others?
what does this suggest about approaches to preventing the
spread of infection?
5/9
Dynamics on networks—SIR disease model
The spread of Severe Acute Respiratory Syndrome (SARS) in 2002–2003.
Netlogo model: Virus on a Network
6/9
Dynamics of networks
The growth model we used for creating scale-free networks and the rewiring model we used for creating small world networks are simple examples of network dynamics
In these models, the state of a node can be unimportant.
More complex dynamic behaviour is possible if both network state
and network structure are changing at the same time.
Consider our SIR disease model on a network:
under what conditions might we expect edges to be rewired? what effect might this have?
7/9
Adaptive networks
For example, consider a road network:
nodes are locations that people travel between
edges are roads between locations that people travel on
roads have a capacity: if two many people travel along a
certain road, it may become congested (a property of the
network’s state)
in response to this congestion, new roads may be built (a
change to the network’s structure)
this may, in turn, cause the patterns of travel to change
8/9
Networks and ABMs
What is the relationship between agent-based models (or multi-agent systems) and networks?
In the simplest case, agents are mapped to the nodes of a network, and the network topology determines patterns of interaction between agents.
Network (as opposed to spatial) models are useful when:
the relationships among agents are more important than their
physical locations; eg, a model of information spreading through a population (potentially via phone or email), versus a model of a fire spreading through a forest
interactions between agents are not grounded in physical
proximity; eg, a model of interacting software agents, versus a
predator-prey model.
What are other complex systems in which network structure may be more appropriate than spatial structure?
9/9