Related papers: Modular networks with hierarchical organization: T…
Previous statistical approaches to hierarchical clustering for social network analysis all construct an "ultrametric" hierarchy. While the assumption of ultrametricity has been discussed and studied in the phylogenetics literature, it has…
A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
Detection of community structures in social networks has attracted lots of attention in the domain of sociology and behavioral sciences. Social networks also exhibit dynamic nature as these networks change continuously with the passage of…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the…
The dynamics of cascading activation, such as rapid changes in public opinion and the outbreak of disease epidemics, have a crucial dependence on the connectivity patterns among the agents. We study cascading dynamics in modular,…
Characterizing large-scale organization in networks, including multilayer networks, is one of the most prominent topics in network science and is important for many applications. One type of mesoscale feature is community structure, in…
We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this…
The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent,…
Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…