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We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
A network's community structure commonly impacts its functions. For instance, networks seeking synchronisation will see this process follow the topology's hierarchical and community structuring. Herein, the interplay of network adjacency…
The power graph $\mathscr{P}(G)$ of a group $G$ is an undirected graph with all the elements of $G$ as vertices and where any two vertices $u$ and $v$ are adjacent if and only if $u=v^m $ or $v=u^m$, $ m \in$ $\mathbb{Z}$. For a simple…
Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…
A hollow matrix described by a graph $G$ is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in $G$. For a given graph $G$, the determination of all possible…
Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…
We study the properties of the eigenvalues of real random matrices and their products. It is known that when the matrix elements are Gaussian-distributed independent random variables, the fraction of real eigenvalues tends to unity as the…
Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
The spectral properties of the adjacency (connectivity) and distance matrix for various types of networks: exponential, scale-free (Albert--Barabasi) and classical random ones (Erdos--Renyi) are evaluated. The graph spectra for dense graph…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse…
In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the…
One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many…