This is a function package for people interested in studying graphs that evolve over time. Anyone with a basic understanding of Python can create their own dynamic graph.

• General info
• Description
• How to define and execute a model
• License

This python package is a dynamic random graphs generator. It allows defining bounded degree dynamic undirected networks i.e., evolving graphs in which each node has bounded degree.

A dynamic graph is a sequence of graphs where the sets of nodes and edges can change at any discrete round. If they can change randomly we call the corresponding random process a dynamic random graph.

Dynamic random graphs analysis allows us to define more accurate models that represent real phenomena.

In these models each node individually execute a distributed protocol in order to maintain a bounded number of connections. It is possible to define " external events " that causes the edge or node disappearance at each time instant.

• RAES ( Request a link, then Accept if Enough Space ) proposed by Becchetti et al. ( More details ) that allows you to define an Expander Graph in O(log n) rounds With High Probability.
• Edge Dynamic (ERAES) proposed by Antonio Cruciani and Francesco Pasquale that is a natural extension of RAES where there exists the probability p that, at each time step, each edge of the graph can fall. This is an infinite stochastic process that allow you to construct a good dynamic Expander Graph.
• Vertex Dynamic (VRAES) proposed by Antonio Cruciani and Francesco Pasquale that is a Dynamic Random Graph where at each time step there are new vertices that join the network and vertices that leave it. This is an infinite stochastic process that allow you to construct a good dynamic Expander Graph.
• Mixed Dynamic (EVRAES) proposed by Antonio Cruciani and Francesco Pasquale. This is a Dynamic Graph model in which nodes and edges appear and disappear. Nodes follow the same rules of VRAES and the edge disappearance phenomenon follows the ERAES scheme.

Given the config.ini file you can set up the the experiments for ERAES and VRAES.

To simulate the EVRAES you can run python mixedDynamic.py. Such simulation is multiprocessing and exploits all your cores. If you want to change the parameters you need to edit the mixedDynamic.py file.

Modify the .ini file under the section: [model]

• graph use ED to define an Edge Dyanamics or VD to define a Vertex Dynamic model

• nodes is the number of nodes of the dynamic random graph. Must be a list of nodes, if more than one integer is in such list the tool will simulate sequentially the model with all the nodes in such list.

• degree is the "target\min" degree that each node must have. Must be a list of integers, if more than one integer is in such list the tool will simulate sequentially the model with all the degrees in such list.

• tolerance is the max degree that each node can have. Can be a list of integers or floats, if more than one value is in such list the tool will simulate sequentially the model with all the tolerances in such list.

• edge_node_falling_probability is the edge-disappearance probability at each round in case of the Edge Dynamics or the node-exiting probability in case of the Vertex Dynamics. Is a list of floats, must be between 0 and 1, if more than one value is in such list the tool will simulate sequentially the model with all the probabilities in such list.

• nodes_poisson_rate is the node-joining rate of the Poisson Process of the Vertex Dynamics. If it is equal to None the tool will use as rates the product of the number of nodes n and the exiting probabilities q. Is a list of floats, if more than one value is in such list the tool will simulate sequentially the model with all the probabilities in such list.

Modify the .ini file under the section: [simulations]

• flooding_protocol If True the protocol will simulate the Flooding process.

• simultaions_number Number of simulation that you want to perform for each fixed model. Must be an integer

• only_spectral_properties If True simulate the model saving only the Spectral Gaps at each round.

• offline_simulation If True saves as a file the adjacency list of the Dynamic Graph before and after the execution of the distributed protocol. WARNING: It performs a high amount of file writings on the disk.

Modify the .ini file under the section: [other_parameters]

• epsilon Float value for the epsilon used by the convergence heuristic in the Edge Dynamic model. NOTE: the Edge Dynamic automatically estimate the epsilon value.

• max_iterations Int value for the maximum number of iteration of the models after their convergence (if you are not simulating the Offline version) or number of steps to perform (if you are simulating the Offline version).

Modify the .ini file under the section: [output_path]

• output_path Output path of the simulations, for EVRAES is ./tmp

Modify the .ini file under the section: [advanced]. Commands for simulating the model on a range of values, every command follows the pattern < min_param , max_param, step_param > where:

• min_param is the minimum value
• max_param is the maximum value
• step_param is the constant increment from min_param to max_param

For example, for:

• min_nodes = 10
• max_nodes = 100
• step_nodes = 20

the tool will simulate the model with the following number of nodes: [10,30,50,70,90]

For executing the model use the command:

                            Python main.py

In order to reproduce the experiments in the paper substitute the config.ini file with the ones in the appropriate folders configurations/EdgeDynamics or configurations/VertexDynamics.

• Spectral properties : model_spectral_conf.ini

• Flooding simulation : model_flooding_simulation.ini

This is free software, if you want to use it please cite this work. Users interested in improving and expanding the project are welcome.

Thanks to Professor Francesco Pasquale for supervising this work.