Related papers: Limit Theorems for Data with Network Structure
Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms…
The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects…
Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…
A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a…
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…
Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…
A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…
This paper analyzes a semiparametric model of network formation in the presence of unobserved agent-specific heterogeneity. The objective is to identify and estimate the preference parameters associated with homophily on observed attributes…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
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…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…