Related papers: Generalized network structures: The configuration …
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the…
Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…
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…
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…
We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of integers, and explore their similarities. We will define a map between the two simplicial complexes,…
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in…
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…
Can neural networks systematically capture discrete, compositional task structure despite their continuous, distributed nature? The impressive capabilities of large-scale neural networks suggest that the answer to this question is yes.…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…
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…
The cornerstone of statistical mechanics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here we formulate a mapping between weighted networks and lattice gasses, making the…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
We present a new model which represents data as a mixture of simplices. Simplices are geometric structures that generalize triangles. We give a simple geometric understanding that allows us to learn a simplicial structure efficiently. Our…
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other…