Degree distribution nearby the origin of a preferential attachment graph.
Degree distributions in general random intersection graphs.
Differential equation approximations for Markov chains.
Discrepancy and eigenvalues of Cayley graphs
We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.
Distances in random graphs with finite mean and infinite variance degrees.
Distinguishing infinite graphs.
Dominating sets of random 2-in 2-out directed graphs.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
Edge cover time for regular graphs.
Edit distance and its computation.
Elementary proofs and the sums differences problem.
In this paper, we rule out the possibility that a certain method of proof in the sums differences conjecture can settle the Kakeya Conjecture.
Encores on cores.
Entrywise bounds for eigenvectors of random graphs.
Enumeration and asymptotic properties of unlabeled outerplanar graphs.
Erdős-Renyi random graphs forest fires self-organized criticality.
Etude du spectre pour certains noyaux sur un arbre
Evolution in random environment and structural instability.
Exact Expectation and Variance of Minimal Basis of Random Matroids
We formulate and prove a formula to compute the expected value of the minimal random basis of an arbitrary finite matroid whose elements are assigned weights which are independent and uniformly distributed on the interval [0, 1]. This method yields an exact formula in terms of the Tutte polynomial. We give a simple formula to find the minimal random basis of the projective geometry PG(r − 1, q).
Expected lengths of minimum spanning trees for non-identical edge distributions.
Fast approximation of centrality.