MultiplexMarkovChain is a Python package that helps discern "dynamical spillover" in multiplex networks.

The package helps discover correlations present in the edge dynamics of multiplex networks. Please see the following paper for information on "dynamical spillover". http://arxiv.org/abs/1505.04766

Requirements

• Numpy
• Networkx
• IPython notebook (for the example)

Main Files

• extract_counts.py : This file contains functions that can extract counts that can be used to construct a Markov chain from longitudinal data on Multiplex networks.
• MultiplexMarkovChain.py : This file contains the class MultiplexMarkovChain. This class helps in building a Markov chain that represents edge dynamics of a multiplex network. The class also has methods to construct the corresponding null model that can determine the existence of dynamical spillover.
• example.ipynb : An example (in IPython notebook format) that steps through how this package can be used to detect dynamical spillover in a real world multiplex network. You can see the example by typing ipython notebook in the command line from the folder in which you cloned the MultiplexMarkovChain repository, then clicking example.ipynb in the browser window that opens.
• alliance_trade_nodes.csv : Contains the data on the presence of nodes (i.e. nation-states) in each year from 1950 to 2003. The format is: year,nation.
• alliance_trade_edges.csv : Contains the data on the presence of alliance and trade edges between a pair of nodes (i.e. nation-states) in each year from 1950 to 2003. The format is: year,nation1,nation2,alliance,trade. alliance, trade are binary entries with 0 indicating absence and 1 indicating presence of that particular type of link between nation1 and nation2.

Unittest files

• test_MultiplexMarkovChain.py : unittests for the classes in the file MultiplexMarkovChain.py.
• test_extract_counts.py : unittests for functions in the file extract_counts.py.
• test_input_edges.csv : Edge list of an example network used as input in unittests.
• test_input_nodes.csv : Node list of an example network used as input in unittests.

Data Sources

The files alliance_trade_nodes.csv and alliance_trade_edges.csv together describe the multiplex network of alliance and trade between countries. The data on international alliances is derived from the ATOP project [B. A. Leeds, Rice University, Department of Political Science, Houston (2005)]. The trade networks are derived from a combination of two datasets on international trade: the Correlates of War (COW) bilateral trade dataset [K. Barbieri, O. M. Keshk, and B. M. Pollins, Conflict Management and Peace Science 26, 471 (2009)], and the Gledistch trade dataset [K. S. Gleditsch, Journal of Conflict Resolution 46, 712 (2002)]. The trade data is binarized such that an edge exists if the value of trade between two countries is greater than 0.001 of the exporter’s GDP. Note the above threshold is not symmetric between the two countries involved in trade, and hence gives us a directed network of trade between nations. Neglecting the edge directionality, i.e., ensuring there is at least one-way trade yields the data provided here.

Acknowledgments

MultiplexMarkovChain thanks Ryan James and Pierre-Andre Noel for helpful pointers.

MultiplexMarkovChain gratefully acknowledges support from the following:

• US Army Research Laboratory and the US Army Research Office under MURI award W911NF-13-1-0340, and Cooperative Agreement W911NF-09-2-0053
• The Defense Threat Reduction Agency Basic Research Grant No. HDTRA1-10-1-0088
• NSF Grant No. ICES-1216048