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We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
Syntax connects words to each other in very specific ways. Two words are syntactically connected if they depend directly on each other. Syntactic connections usually happen within a sentence. Gathering all those connection across several…
The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
Network science provides an indispensable theoretical framework for studying the structure and function of real complex systems. Different network models are often used for finding the rules that govern their evolution, whereby the correct…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution…
New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we…
Understanding the process by which the individuals of a society make up their minds and reach opinions about different issues can be of fundamental importance. In this work we propose an idealized model for competitive cluster growth in…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter…
We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and interconnections strength. It is well-known that the topology of a network affects its resilience to…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
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 the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…