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Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Self-regulation of living tissue as an example of self-organization phenomena in active fractal systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…
The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
The conformation space of a 20-residue antiparallel $\beta$-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…
We address the role of topology in the energy transport process that occurs in networks of photosynthetic complexes. We take inspiration from light harvesting networks present in purple bacteria and simulate an incoherent dissipative energy…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…