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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…

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…

To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract…

Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…

Networks in nature possess a remarkable amount of structure. Via a series of data-driven discoveries, the cutting edge of network science has recently progressed from positing that the random graphs of mathematical graph theory might…

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…

A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is…

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups…

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…

The ability to detect weak distributed activation patterns in networks is critical to several applications, such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces of a biochemical spread…

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…

Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many…

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…

In the study of networked systems such as biological, technological, and social networks the available data are often uncertain. Rather than knowing the structure of a network exactly, we know the connections between nodes only with a…

Humans are social by nature. Throughout history, people have formed communities and built relationships. Most relationships with coworkers, friends, and family are developed during face-to-face interactions. These relationships are…