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The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…
We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent…
Monitoring edge-geodetic sets in a graph are subsets of vertices such that every edge of the graph must lie on all the shortest paths between two vertices of the monitoring set. These objects were introduced in a work by Foucaud, Krishna…
Finding dense subgraphs is a core problem with numerous graph mining applications such as community detection in social networks and anomaly detection. However, in many real-world networks connections are not equal. One way to label edges…
A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…
The network interference model for causal inference places all experimental units at the vertices of an undirected exposure graph, such that treatment assigned to one unit may affect the outcome of another unit if and only if these two…
We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs…
Functional connectivity (FC) has been widely used to study brain network interactions underlying the emerging cognition and behavior of an individual. FC is usually defined as the correlation or partial correlation between brain regions.…
We analyze the identifiability of directed acyclic graphs in the case of partial excitation and measurement. We consider an additive model where the nonlinear functions located in the edges depend only on a past input, and we analyze the…
In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
New Matlab functions for network centrality are introduced. Instead of the mean distance, the generalized mean distance is used. If closer relationships are prioritized, this closeness measure is also defined for unconnected graphs. Instead…
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…
Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the…
Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we…
Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…
We study a class of directed random graphs. In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points in the interval (y,x] which are chosen uniformly with density one. We analyze…
This paper investigates the influence of directed networks on decentralized stochastic non-convex optimization associated with column-stochastic mixing matrices. Surprisingly, we find that the canonical spectral gap, a widely used metric in…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…