Related papers: k-core organization of complex networks
Graphs have been widely used in many applications such as social networks, collaboration networks, and biological networks. One important graph analytics is to explore cohesive subgraphs in a large graph. Among several cohesive subgraphs…
In many complex systems, the interactions between objects span multiple aspects. Multiplex networks are accurate paradigms to model such systems, where each edge is associated with a type. A key graph mining primitive is extracting dense…
We introduce and use k-shell decomposition to investigate the topology of the Internet at the AS level. Our analysis separates the Internet into three sub-components: (a) a nucleus which is a small (~100 nodes) very well connected globally…
The air transportation network, a fundamental component of critical infrastructure, is formed from a collection of individual air carriers, each one with a methodically designed and engineered network structure. We analyze the individual…
In this paper we consider $j$-tuple-connected components in random $k$-uniform hypergraphs (the $j$-tuple-connectedness relation can be defined by letting two $j$-sets be connected if they lie in a common edge and consider the transitive…
Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability p, independently of each other, and a deterministic spreading rule with a fixed parameter k: if a vacant site has…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
A {\em $k$-kernel} in a digraph $G$ is a stable set $X$ of vertices such that every vertex of $G$ can be joined from $X$ by a directed path of length at most $k$. We prove three results about $k$-kernels. First, it was conjectured by…
In this work we continue the investigation launched in [FHR16] of the structural properties of the structural properties of the Layers model, a dependent percolation model. Given an undirected graph $G=(V,E)$ and an integer $k$, let…
The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional…
The tree of decomposition of a $k$-connected graph by a set $\mathfrak S$ of pairwise independent $k$-vertex cutsets is defined as follows. The vertices of this tree are cutsets of $\mathfrak S$ and parts of decomposition of the graph by…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…
One interesting question is how a graph develops from some constrained random graph process, which is a fundamental mechanism in the formation and evolution of dynamic networks. The problem here is referred to the random $K_k$-removal…
Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…
We study the problem of finding the smallest set of nodes in a network whose removal results in an empty $k$-core; where the $k$-core is the sub-network obtained after the iterative removal of all nodes of degree smaller than $k$. This…