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As two main focuses of the study of complex networks, the community structure and the dynamics on networks have both attracted much attention in various scientific fields. However, it is still an open question how the community structure is…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other…
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks.…
Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion,…
To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving…
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
Innovation emerges from complex collaboration patterns - among inventors, firms, or institutions. However, not much is known about the overall mesoscopic structure around which inventive activity self-organizes. Here, we tackle this problem…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…
Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a…
The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as…
In network science, assortativity refers to the tendency of links to exist between nodes with similar attributes. In social networks, for example, links tend to exist between individuals of similar age, nationality, location, race, income,…
Characterizing the community structure of complex networks is a key challenge in many scientific fields. Very diverse algorithms and methods have been proposed to this end, many working reasonably well in specific situations. However, no…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
The detection of community structure is probably one of the hottest trends in complex network research as it reveals the internal organization of people, molecules or processes behind social, biological or computer networks\dots The issue…
We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…