Consider a preferential attachment model for network evolution that allows both node and edge arrival events: at time t, with probability pt a new node arrives and a new edge is added between the new node and an existing node, and with probability 1 - pt a new edge is added between two existing nodes. In both cases existing nodes are chosen at random according to preferential attachment, i.e., with probability proportional to their degree. For δ ∈ (0, 1), the δ-founders of the network at time t is the minimal set of the first nodes to enter the network (i.e., founders) guaranteeing that the sum of degrees of nodes in the set is at least a δ fraction of the number of edges in the graph at time t. We show that for the common model where pt is constant, i.e., when pt = p for every t and the network is sparse with linear number of edges, the size of the δ-founders set is concentrated around δ2/pnt, and thus is linear in nt, the number of nodes at time t. In contrast, we show that for pt = min{1, (equation found)} and when the network is dense with super-linear number of edges, the size of the δ-founders set is sub-linear in nt and concentrated around (image found)((nt)η), where η = δ1/a
CITATION STYLE
Avin, C., Lotker, Z., Nahum, Y., & Peleg, D. (2015). Core size and densification in preferential attachment networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9135, pp. 492–503). Springer Verlag. https://doi.org/10.1007/978-3-662-47666-6_39
Mendeley helps you to discover research relevant for your work.