Related papers: Structural Balance and Random Walks on Complex Net…

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By…

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…

We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically,…

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…

Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving…

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…

Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…

We investigate signed networks with community structure with respect to their spectrum and their evolution under a dynamical model of structural balance, a prominent theory of signed social networks. The spectrum of the adjacency matrix…

Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…

The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be…

Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…

In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…

Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…