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In neural networks with identical neurons, the matrix of connection weights completely describes the network structure and thereby determines how it is processing information. However, due to the non-linearity of these systems, it is not…
A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…
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…
Multiplex networks are a powerful framework for representing systems with multiple types of interactions among a common set of entities. Understanding their structure requires statistical tools capturing higher-order cross-layer…
Several natural and theoretical networks can be broken down into smaller portions, or subgraphs corresponding to neighborhoods. The more frequent of these neighborhoods can then be understood as motifs of the network, being therefore…
The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops,…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
In the past years statistical physics has been successfully applied for complex networks modelling. In particular, it has been shown that the maximum entropy principle can be exploited in order to construct graph ensembles for real-world…
Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and…
When studying a complex system it is often useful to think of the system as a network of interacting units. One can then ask if some properties of the entire network are already explained by a small part of the network - a network motif. A…
The structure of complex networks can be characterized by counting and analyzing network motifs. Motifs are small subgraphs that occur repeatedly in a network, such as triangles or chains. Recent work has generalized motifs to temporal and…
We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992-2003 period. We compare structures across commodities and time by means of the normalized mutual information…
Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the…
Production networks arise from supply and customer relations among firms. These systems are gaining growing attention as a consequence of disruptions due to natural or man-made disasters that happened in the last years, such as the Covid-19…
Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks,…
Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are…
Networks are fundamental for our understanding of complex systems. Interactions between individual nodes in networks generate network motifs - small recurrent patterns that can be considered the network's building-block components,…
The structure of the supply chain network has important implications for modelling economic systems, from growth trajectories to responses to shocks or natural disasters. However, reconstructing firm-to-firm networks from available…
In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the…
In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an…