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Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…
We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Network representation learning (also known as information network embedding) has been the central piece of research in social and information network analysis for the last couple of years. An information network can be viewed as a linked…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
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)…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Social networks exhibit strikingly systematic patterns across a wide range of human contexts. While genetic variation accounts for a significant portion of the variation in many complex social behaviors, the heritability of egocentric…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
Topological electromagnetism owing to nontrivial momentum-space topology of electrons in insulators gives rise to diverse anomalous magnetoelectric responses. While conventional inductors and capacitors are based on classical…
The behaviour of electrical networks can be described with many different representations, each with their distinct benefits. In this paper, we consider Z, Y, G, H, ABCD, S and T parameters. Formulas exist to go from one representation to…
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the sum of the incoming currents is set to be zero in each pair.…
How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale we consider the coherence of overall network dynamics. We show that such \emph{global coherence}…
The statistical tools of Complex Network Analysis are of great use to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention…