Related papers: Temporal Triadic Closure: Finding Dense Structures…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
Given an infinite connected regular graph $G=(V,E)$, place at each vertex Pois($\lambda$) walkers performing independent lazy simple random walks on $G$ simultaneously. When two walkers visit the same vertex at the same time they are…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph can be represented…
We propose new graph representations that exploit dense local structure to improve time and space simultaneously. Given an undirected graph $G$, we define a dual clique cover (DCC) representation of $G$ to be the pair $(C, L)$, where $C$ is…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Searching for local communities is an important research challenge that allows for personalized community discovery and supports advanced data analysis in various complex networks, such as the World Wide Web, social networks, and brain…
Temporal graphs represent binary relationships that change along time. They can model the dynamism of, for example, social and communication networks. Temporal graphs are defined as sets of contacts that are edges tagged with the temporal…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a…
We show that the algorithm presented in [J. Fox, T. Roughgarden, C. Seshadhri, F. Wei, and N. Wein. Finding cliques in social networks: A new distribution-free model. SIAM journal on computing, 49(2):448-464, 2020.] can be modified to have…
We address the problem of testing whether a given dynamic graph is temporally connected, {\it i.e} a temporal path (also called a {\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the…
Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
Finding meaningful communities - subnetworks of interest within a large scale network - is a problem with a variety of applications. Most existing work towards community detection focuses on a single network. However, many real-life…
We consider a distance-regular graph $\G$ with diameter $d \ge 3$ and eigenvalues $k=\theta_0>\theta_1>... >\theta_d$. We show the intersection numbers $a_1, b_1$ satisfy $$ (\theta_1 + {k \over a_1+1}) (\theta_d + {k \over a_1+1}) \ge -…
Many types of dynamic networks are made up of durable entities whose links evolve over time. When considered from a {\em global} and {\em discrete} standpoint, these networks are often modelled as evolving graphs, i.e. a sequence of graphs…
We define the following parameter of connected graphs. For a given graph $G$ we place one agent in each vertex of $G$. Every pair of agents sharing a common edge is declared to be acquainted. In each round we choose some matching of $G$…
In this work we consider temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of integers. The labels of an edge indicate the discrete moments in time at which the edge is available. We…
Graphs form a natural model for relationships and interactions between entities, for example, between people in social and cooperation networks, servers in computer networks, or tags and words in documents and tweets. But, which of these…