Related papers: Towards a Better Understanding of Large Scale Netw…
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 derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
This paper studies networks where all nodes are distributed on a unit square $A\triangleq[(-1/2,1/2)^{2}$ following a Poisson distribution with known density $\rho$ and a pair of nodes separated by an Euclidean distance $x$ are directly…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is…
This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
Network datasets typically exhibit certain types of statistical dependencies, such as within-dyad correlation, row and column heterogeneity, and third-order dependence patterns such as transitivity and clustering. The first two of these can…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
Distributed configuration management is imperative for wireless infrastructureless networks where each node adjusts locally its physical and logical configuration through information exchange with neighbors. Two issues remain open. The…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…