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Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…

In this work we present a model for evolving networks, where the driven force is related to the social affinity between individuals in a population. In the model, a set of individuals initially arranged on a regular ordered network and thus…

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown…

Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…

Top-N recommendation aims to recommend each consumer a small set of N items from a large collection of items, and its accuracy is one of the most common indexes to evaluate the performance of a recommendation system. While a large number of…

We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been…

The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…

The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability $p$. In order to discriminate the better and…

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…

Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the…

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to…

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…

In this paper, we tackle a challenging problem inherent in a series of applications: tracking the influential nodes in dynamic networks. Specifically, we model a dynamic network as a stream of edge weight updates. This general model…

A remarkable phenomenon in the time evolution of many networks such as cultural, political, national and economic systems, is the recurrent transition between the states of union and division of nodes. In this work, we propose a…

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…

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive…

We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…