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A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
From many datasets gathered in online social networks, well defined community structures have been observed. A large number of users participate in these networks and the size of the resulting graphs poses computational challenges. There is…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model…
Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…
The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single…
This article presents a novel approach for learning low-dimensional distributed representations of users in online social networks. Existing methods rely on the network structure formed by the social relationships among users to extract…
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a…
Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…
In recent years, people spend a lot of time on social networks. They use social networks as a place to comment on personal or public events. Thus, a large amount of information is generated and shared daily in these networks. Using such a…
When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
The massive amount of text data on the web has facilitated research on the quantitative analysis of public opinion, which could not be visualized earlier. In this paper, we propose a new opinion dynamics theory. This theory that is intended…