Algebraic Analysis of Multiple Social Networks with multiplex
Journal of Statistical Software
multiplex is a computer program that provides algebraic tools for the analysis of multiple network structures within the R environment. Apart from the possibility to create and manipulate multivariate data representing multiplex, signed, and two-mode networks, this package offers a collection of functions that deal with algebraic systems -such as the partially ordered semigroup, and balance or cluster semirings -their decomposition, and the enumeration of bundle patterns occurring at different
... rring at different levels of the network. Moreover, through Galois derivations between families of the pairs of subsets in different domains it is possible to analyze affiliation networks with an algebraic approach. Visualization of multigraphs, different forms of bipartite graphs, inclusion lattices, Cayley graphs is supported as well with related packages. The algebraic representation of these particular systems serves to uncover their "relational interlock," which is represented by different types of algebraic constraints, and that allows making a substantial interpretation of the network structure. In this paper, particular types of complex systems studied within an algebraic approach are multiplex networks with different kinds of positively valued relations, signed networks with ties having opposite valences, and affiliation networks that are arrangements with two domains, one for the actors and the other for events or categories. Apart from the well-known computer programs for the analysis of social networks like UCINET (Borgatti, Everett, and Freeman 2002), Pajek (Batagelj and Mrvar 1998), and PNet (Wang, Pattison, and Robins 2009), there is a number of packages for making diverse types of social network analyzes within the R environment (R Core Team 2019). Notably, sna (Butts 2008a,b) and igraph (Csardi and Nepusz 2006) are popular within the social network analysis community, not only for measuring structural indices of equivalence or distance, but also for the visualization of graphs representing the network structure. A more strictly statistical approach for the analysis of network data is found in statnet (Handcock, Hunter, Butts, Goodreau, and Morris 2008) and its related packages, particularly ergm (Hunter, Handcock, Butts, Goodreau, and Morris 2008) that can simulate and fit networks based on exponential random graph models, whereas RSiena (Ripley, Boitmanis, Snijders, Schoenenberger, and Niezink 2020) is the R implementation of the stochastic actor oriented model (Snijders 2001) for dynamic networks. Other programs that have focus on multiple network structures are MuxViz (De Domenico et al. 2017), Multidimensional Network Analysis (Coscia 2017), and Multilayer Networks Library (Kivelä 2017). The former combines R with GNU Octave, whereas the other two platforms are Java and Python libraries, respectively.