Related papers: Density decompositions of networks
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…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
Liquid water, besides being fundamental for life on Earth, has long fascinated scientists due to several anomalies. Different hypotheses have been put forward to explain these peculiarities. The most accredited one foresees the presence in…
A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes…
Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…
One of the main issues in modern network science is the phenomenon of cascading failures of a small number of attacks. Here we define the dimension of a network to be the maximal number of functions or features of nodes of the network. It…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
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…
Over the past decade, Internet centralization and its implications for both people and the resilience of the Internet has become a topic of active debate. While the networking community informally agrees on the definition of centralization,…
Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…
Interpretability of Deep Neural Networks has become a major area of exploration. Although these networks have achieved state of the art accuracy in many tasks, it is extremely difficult to interpret and explain their decisions. In this work…
The ability to share social network data at the level of individual connections is beneficial to science: not only for reproducing results, but also for researchers who may wish to use it for purposes not foreseen by the data releaser.…
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…