Let G = (V, E) denote a simple graph with vertex set V and edge set E. The profile of a vertex set V' subset of V denotes the multiset of pairwise distances between the vertices of V'. Two disjoint subsets of V are homometric if their profiles are the same ...
Modern data processing tasks frequently involve structured data, for example signals defined on the vertex set of a weighted graph. In this paper, we address the problem of inference of mobility patterns from data defined on geographical graphs based on sp ...
In a seminal paper published in 1946, Erd ̋os initiated the investigation of the distribution of distances generated by point sets in metric spaces. In spite of some spectacular par- tial successes and persistent attacks by generations of mathe- maticians, ...
Graph matching is a generalization of the classic graph isomorphism problem. By using only their structures a graph-matching algorithm finds a map between the vertex sets of two similar graphs. This has applications in the de-anonymization of social and in ...
We derive a framework for sampling online communities based on the mean hitting time of its members, considering that there are multiple graphs associated with the same vertex set V representing the social network. First, we formulate random walk models on ...
Given a collection C of curves in the plane, its string graph is defined as the graph with vertex set C, in which two curves in C are adjacent if and only if they intersect. Given a partially ordered set (P,
The intersection graph of a collection C of sets is the graph on the vertex set C, in which C-1 . C-2 is an element of C are joined by an edge if and only if C-1 boolean AND C-2 not equal empty set. Erdos conjectured that the chromatic number of triangle-f ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conj ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
Mobile phone data provides rich dynamic information on human activities in social network analysis. In this paper, we represent data from two different modalities as a graph and functions defined on the vertex set of the graph. We propose a regularization ...
