Related papers: The topological relationship between the large-sca…

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…

A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the…

Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…

Understanding of the mechanisms driving our daily face-to-face encounters is still limited; the field lacks large-scale datasets describing both individual behaviors and their collective interactions. However, here, with the help of travel…

The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…

The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…

Network motifs are small building blocks of complex networks. Statistically significant motifs often perform network-specific functions. However, the precise nature of the connection between motifs and the global structure and function of…

Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

Large-scale human social network structure is typically inferred from digital trace samples of online social media platforms or mobile communication data. Instead, here we investigate the social network structure of a complete population,…

Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…

Network motifs can capture basic interaction patterns and inform the functional properties of networks. However, real-world complex systems often have multiple types of relationships, which cannot be represented by a monolayer network. The…

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…

In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…