Core size and densification in preferential attachment networks

Chen Avin; Zvi Lotker; Yinon Nahum; David Peleg

doi:10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks

Chen Avin, Zvi Lotker, Yinon Nahum, David Peleg

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 - p_t 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 p_t is constant, i.e., when p_t = 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/^pn_t, and thus is linear in n_t, the number of nodes at time t.

Original language	American English
Title of host publication	Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
Editors	Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama, Magnus M. Halldorsson
Publisher	Springer Verlag
Pages	492-503
Number of pages	12
ISBN (Print)	9783662476659
DOIs	https://doi.org/10.1007/978-3-662-47666-6_39
State	Published - 1 Jan 2015
Event	42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan Duration: 6 Jul 2015 → 10 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9135

Conference

Conference	42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
Country/Territory	Japan
City	Kyoto
Period	6/07/15 → 10/07/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

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

Cite this

Avin, C., Lotker, Z., Nahum, Y., & Peleg, D. (2015). Core size and densification in preferential attachment networks. In N. Kobayashi, B. Speckmann, K. Iwama, & M. M. Halldorsson (Eds.), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings (pp. 492-503). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9135). Springer Verlag. https://doi.org/10.1007/978-3-662-47666-6_39

Avin, Chen ; Lotker, Zvi ; Nahum, Yinon et al. / Core size and densification in preferential attachment networks. Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. editor / Naoki Kobayashi ; Bettina Speckmann ; Kazuo Iwama ; Magnus M. Halldorsson. Springer Verlag, 2015. pp. 492-503 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "Chen Avin and Zvi Lotker and Yinon Nahum and David Peleg",

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Avin, C , Lotker, Z, Nahum, Y & Peleg, D 2015, Core size and densification in preferential attachment networks. in N Kobayashi, B Speckmann, K Iwama & MM Halldorsson (eds), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9135, Springer Verlag, pp. 492-503, 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, Kyoto, Japan, 6/07/15. https://doi.org/10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks. / Avin, Chen ; Lotker, Zvi; Nahum, Yinon et al.
Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. ed. / Naoki Kobayashi; Bettina Speckmann; Kazuo Iwama; Magnus M. Halldorsson. Springer Verlag, 2015. p. 492-503 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9135).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Peleg, David

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PY - 2015/1/1

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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.

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

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Y2 - 6 July 2015 through 10 July 2015

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Avin C , Lotker Z, Nahum Y, Peleg D. Core size and densification in preferential attachment networks. In Kobayashi N, Speckmann B, Iwama K, Halldorsson MM, editors, Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. Springer Verlag. 2015. p. 492-503. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks

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