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Many biological phenomena or social events critically depend on how information evolves in complex networks. However, a general theory to characterize information evolution is yet absent. Consequently, numerous unknowns remain about the…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…
Disentangling the mechanisms underlying the social network evolution is one of social science's unsolved puzzles. Preferential attachment is a powerful mechanism explaining social network dynamics, yet not able to explain all scaling-laws…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
This survey presents the main results achieved for the influence maximization problem in social networks. This problem is well studied in the literature and, thanks to its recent applications, some of which currently deployed on the field,…
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Social media provides a rich source of networked data. This data is represented by a set of nodes and a set of relations (edges). It is often possible to obtain or infer multiple types of relations from the same set of nodes, such as…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
This paper theoretically investigates the following empirical phenomenon: given a high-complexity network with poor generalization bounds, one can distill it into a network with nearly identical predictions but low complexity and vastly…
Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or adopt the information, observing individual…
The preferential attachment (PA) process is a popular theory for explaining network power-law degree distributions. In PA, the probability that a new vertex adds an edge to an existing vertex depends on the connectivity of the target…
Information diffusion is a fundamental process that takes place over networks. While it is rarely realistic to observe the individual transmissions of the information diffusion process, it is typically possible to observe when individuals…
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…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…