TY - GEN

T1 - Core size and densification in preferential attachment networks

AU - Avin, Chen

AU - Lotker, Zvi

AU - Nahum, Yinon

AU - Peleg, David

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84950136198&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-47666-6_39

DO - 10.1007/978-3-662-47666-6_39

M3 - Conference contribution

AN - SCOPUS:84950136198

SN - 9783662476659

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 492

EP - 503

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

A2 - Kobayashi, Naoki

A2 - Speckmann, Bettina

A2 - Iwama, Kazuo

A2 - Halldorsson, Magnus M.

PB - Springer Verlag

T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Y2 - 6 July 2015 through 10 July 2015

ER -