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Although most networks in nature exhibit complex topology the origins of such complexity remains unclear. We introduce a model of a growing network of interacting agents in which each new agent's membership to the network is determined by…

In a decentralized machine learning system, data is typically partitioned among multiple devices or nodes, each of which trains a local model using its own data. These local models are then shared and combined to create a global model that…

During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small' in the sense…

Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have…

Consider a communication network to which a sequence of self-interested users come and send requests for data transmission between nodes. This work studies the question of how to guide the path selection choices made by those…

Centrality of a node measures its relative importance within a network. There are a number of applications of centrality, including inferring the influence or success of an individual in a social network, and the resulting social network…

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of…

By studying varies dynamical processes, including coupled maps, cellular automata and coupled differential equations, on five different kinds of known networks, we found a positive relation between signal correlation and node's degree. Thus…

Social network position confers power and social capital. In the setting of online social networks that have massive reach, creating mathematical representations of social capital is an important step towards understanding how network…

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

We present an agent-based model of microscopic wealth exchange in a dynamic network to study the topological features associated with economic inequality. The model evolves through two alternating processes, the conservative exchange of…

Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…

Many classes of network growth models have been proposed in the literature for capturing real-world complex networks. Existing research primarily focuses on global characteristics of these models, e.g., degree distribution. We aim to shift…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…

Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration…