Related papers: Detecting weighted hidden cliques
Finding the largest clique is a notoriously hard problem, even on random graphs. It is known that the clique number of a random graph G(n,1/2) is almost surely either k or k+1, where k = 2log n - 2log(log n) - 1. However, a simple greedy…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable…
In this paper, we prove a sharp limit on the community detection problem with colored edges. We assume two equal-sized communities and there are $m$ different types of edges. If two vertices are in the same community, the distribution of…
Cliques are defined as complete graphs or subgraphs; they are the strongest form of cohesive subgroup, and are of interest in both social science and engineering contexts. In this paper we show how to efficiently estimate the distribution…
Identifying differences in networks has become a canonical problem in many biological applications. Here, we focus on testing whether two Gaussian graphical models are the same. Existing methods try to accomplish this goal by either…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
We get central limit type theorems for the total number of edges in the generalized random graphs with random vertex weights under different moment conditions on distributions of the weights.
The edge clique cover (ECC) problem -- where the goal is to find a minimum cardinality set of cliques that cover all the edges of a graph -- is a classic NP-hard problem that has received much attention from both the theoretical and…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
Cliques, or fully connected subgraphs, are among the most important and well-studied graph motifs in network science. We consider the problem of finding a statisti- cally anomalous clique hidden in a large network. There are two parts to…
In 1966, Erd\H{o}s, Goodman, and P\'{o}sa showed that if $G$ is an $n$-vertex graph, then at most $\lfloor n^2/4 \rfloor$ cliques of $G$ are needed to cover the edges of $G$, and the bound is best possible as witnessed by the balanced…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
In the classical partial vertex cover problem, we are given a graph $G$ and two positive integers $R$ and $L$. The goal is to check whether there is a subset $V'$ of $V$ of size at most $R$, such that $V'$ covers at least $L$ edges of $G$.…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
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…