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Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and…

The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…

Community structure is a typical property of many real-world networks, and has become a key to understand the dynamics of the networked systems. In these networks most nodes apparently lie in a community while there often exists a few nodes…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…

Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in…

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes…

To understand the structure of a large-scale biological, social, or technological network, it can be helpful to decompose the network into smaller subunits or modules. In this article, we develop an information-theoretic foundation for the…

Over the past decade network theory has turned out to be a powerful methodology to investigate complex systems of various sorts. Through data analysis, modeling, and simulation quite an unparalleled insight into their structure, function,…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

Modelling relationships between entities in real-world systems with a simple graph is a standard approach. However, reality is better embraced as several interdependent subsystems (or layers). Recently the concept of a multilayer network…

In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

Networks are pervasive in the real world. Nature, society, economy, and technology are supported by ostensibly different networks that in fact share an amazing number of interesting structural properties. Network thinking exploded in the…

In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…

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…

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or…