Related papers: Localization in random bipartite graphs: numerical…
Homophily, the tendency of individuals who are alike to form ties with one another, is an important concept in the study of social networks. Yet accounting for homophily effects is complicated in the context of bipartite networks where ties…
A set $S$ of vertices of a graph $G$ is \emph{distinguishing} if the sets of neighbors in $S$ for every pair of vertices not in $S$ are distinct. A \emph{locating-dominating set} of $G$ is a dominating distinguishing set. The…
We study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and the…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
In this paper we study the local law for eigenvalues of large random regular bipartite graphs with degree growing arbitrarily fast. We prove that the empirical spectral distribution of the adjacency matrix converges to a scaled down copy of…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
This paper analyzes different online algorithms for the problem of assigning weights to edges in a fully-connected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear…
In this paper, we analyze the exact asymptotic behavior of the connectivity probability in a random binomial bipartite graph $G(n,m,p)$ under various regimes of the edge probability $p=p(n)$. To determine this probability, a method based on…
We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the…
We propose a formal graph-theoretic model for studying the problem of matching rides online in a ride-sharing platform. Unlike most of the literature on online matching, our model, that we call {\em Online Windowed Non-Bipartite Matching}…
We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
A \emph{Stick graph} is an intersection graph of axis-aligned segments such that the left end-points of the horizontal segments and the bottom end-points of the vertical segments lie on a `ground line,' a line with slope $-1$. It is an open…
In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…
The binomial random bipartite graph $G(n,n,p)$ is the random graph formed by taking two partition classes of size $n$ and including each edge between them independently with probability $p$. It is known that this model exhibits a similar…
The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…