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The issue of network community detection has been extensively studied across many fields. Most community detection methods assume that nodes belong to only one community. However, in many cases, nodes can belong to multiple communities…
Research into detection of dense communities has recently attracted increasing attention within network science, various metrics for detection of such communities have been proposed. The most popular metric -- Modularity -- is based on the…
Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios,…
Correlation networks derived from multivariate data appear in many applications across the sciences. These networks are usually dense and require sparsification to detect meaningful structure. However, current methods for sparsifying…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
Complex networks often have a modular structure, where a number of tightly- connected groups of nodes (modules) have relatively few interconnections. Modularity had been shown to have an important effect on the evolution and stability of…
Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes…
Large-scale blockages like buildings affect the performance of urban cellular networks, especially at higher frequencies. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of…
We present a framework for automatically decomposing ("block-modeling") the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph ("block model") depicting the main patterns of…
In this note, we introduce the notion of modulus of $p$-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain…
It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as…
This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are…
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph…
We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale…
Monadic stability and the more general monadic dependence (or NIP) are tameness conditions for classes of logical structures, studied in the 80's in Shelah's classification program in model theory. They recently emerged in algorithmic and…
For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on $\mathrm{Bun}_P$, the moduli stack of $P$-bundles on the Fargues--Fontaine…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…