Related papers: Non-random network connectivity comes in pairs
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among…
We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
Social networks have been of much interest in recent years. We here focus on a network structure derived from co-occurrences of people in traditional newspaper media. We find three clear deviations from what can be expected in a random…
Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated using model neurons with simple connection topology…
In a wide range of complex networks, the links between the nodes are temporal and may sporadically appear and disappear. This temporality is fundamental to analyze the formation of paths within such networks. Moreover, the presence of the…
we study the statistical properties of inhomogenous Poisson networks. we perform a detailed analysis of the statistical properties of Poisson networks and show that the topological properties of random cellular structures, can be derived…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To…
An unexpected and somewhat surprising observation is that two counter-cascaded systems, given the right conditions, can exhibit multivaluedness from one of the outputs to the other. The main result presented here is a necessary and…
Over the past years, network science has proven invaluable as a means to better understand many of the processes taking place in the brain. Recently, interareal connectivity data of the macaque cortex was made available with great richness…
In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to…
We consider the non-crossing connectors problem, which is stated as follows: Given n simply connected regions R_1,...,R_n in the plane and finite point sets P_i subset of R_i for i=1,...,n, are there non-crossing connectors y_i for…
Bipartite networks provide a major insight into the organisation of many real-world systems. One of the most relevant issues encountered when modelling a bipartite network is that of facing the information shortage concerning intra-layer…