Graphlets in Multiplex Networks

Abstract

We develop graphlet analysis for multiplex networks and discuss how this analysis can be extended to multilayer and multilevel networks as well as to graphs with node and/or link categorical attributes. The analysis has been adapted for two typical examples of multiplexes: economic trade data represented as a 957-plex network and 75 social networks each represented as a 12-plex network. We show that wedges (open triads) occur more often in economic trade networks than in social networks, indicating the tendency of a country to produce/trade of a product in local structure of triads which are not closed. Moreover, our analysis provides evidence that the countries with small diversity tend to form correlated triangles. Wedges also appear in the social networks, however the dominant graphlets in social networks are triangles (closed triads). If a multiplex structure indicates a strong tie, the graphlet analysis provides another evidence for the concepts of strong/weak ties and structural holes. In contrast to Granovetter's seminal work on the strength of weak ties, in which it has been documented that the wedges with only strong ties are absent, here we show that for the analyzed 75 social networks, the wedges with only strong ties are not only present but also significantly correlated.

Modelling a multiplex brain network by local transfer entropy

“…The influence of the network structure on dynamical processes can be estimated by appropriate indexes in the framework of the analysis of reciprocity 35 – 37 (RI) and of subgraphs 38 , 39 . The RI estimates the occurrence of mutual relationships among node pairs looking at the number of reciprocal links normalized to the total number of links 35 .…”

“…Concerning subgraphs, the recent introduction of graphlets 38 , suggests the following definition of a subgraph: a combination of in- and out-links within a set of connected nodes where double links are not allowed. Notice that different combinations of in- and out-links can draw the same geometric pattern, called isomorphic, to be counted only once (see Fig.…”

Modelling a Multiplex Brain Network by Local Transfer Entropy

“…In summary, RI values normalized to a nullmodel network in the range [+1, -1] (see the Statistical Analysis Section below) indicate: -reciprocate connections (RI > 0); -reciprocation avoidance (RI < 0); -independent behaviour (RI = 0). Concerning subgraphs, the recent introduction of graphlets 36 , suggests the following definition of a subgraph: a combination of in-and out-links within a set of connected nodes where double links are not allowed. Notice that different combinations of in-and out-nodes can draw the same geometric pattern, called isomorphic, to be counted only once (see Fig.…”

“…The influence of the network structure on dynamical processes can be estimated by appropriate indexes in the framework of the analysis of reciprocity 33,34,35 (RI) and of subgraphs 36,37 . The RI estimates the occurrence of mutual relationships among node pairs looking at the number of reciprocal links normalized to the total number of links 33 .…”

Applications of statistical physics theories on research and innovation networks

“…They have been used in various studies, especially for analyzing network structure. Antal et al [141] use triads to study the dynamics of a social network, Lambiotte et al [142] make use of triangles for geographic analysis of a mobile phone communication network and for studying its cohesion, Zhang et al [143] use a triangle-based metric to examine the stability of a network, and Dimitrova et al [144] use triangles for the structural analysis of various multiplex networks.…”