Decapitation of networks with and without weights and direction : The economics of iterated attack and defense Advisor : Professor Frank Y. S. Lin Presented by: Tuan-Chun Chen Presentation date: Mar. 6,

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 2

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 3

Introduction Many empirically observed networks can be modeled as scale-free networks. Ex: peer-to- peer networks Scale-free networks are more robust against random attacks than targeted attacks. 4

Introduction Betweenness centrality can be an alternative to degree for attack targeting. A dynamic case : each round an attacker removes a certain number of nodes, but the defenders can recruit other nodes to replace the lost ones. The smaller the largest connected component after an attack-defense round, the more successful is the attack. 5

Introduction Two attacks were examined: Removal of high-degree nodes Path centrality attack -> Combine cliques with delegation is most effective -> Defense strategies (i) Radom replacement > less than 3 rounds (ii) Ring replacement > 3~12 rounds (iii) Clique replacement > robust 6

Introduction Contribution and plan of this paper: Extend the former research to consider weighted and directed networks and regards the economic aspects of the attack and defense strategies. 7

Introduction Reasons to consider weights and directions : Delegation strategies and the computation of node centralities may depend on the weight of the links. The distance between nodes may also be relevant to assess the impact of an attack on the LCC(Largest Connected Component). 8

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 9

Economic model Attacks and their cost: kThe number of nodes destroyed in an attack C FA Fixed cost incurred to locate the target nodes CXCX Cost of destroying one node 10

Economic model Locating target nodes by measuring criticality of nodes: ◦ node degree ◦ node path centrality ◦ in the case of weighted : R(i)The reliability of a node I F ij The weight of most reliable path between i and j 11

Economic model Defenses and their cost C FD Fixed cost of starting a defense round C del (h[, q])Cost of implementing delegation for nodes with criticality δ higher than h hThreshold criticality qThe clique size in case delegation is based on cliques C cli (q) Cost of replacing each destroyed nodes by a clique consisting of q new nodes. 12

Economic model Delegation strategies and their cost (i)Before attacks start (ii)Each time new edges are added to the network due to the defense strategy of clique formation 13

Economic model (i) Before attacks start ◦ Node criticality is measured as node degree. ◦ A node i with degree δ (i) > h attempts to transfer some of its edges to its neighbors. 14

Economic model 15

Economic model (i) Before attacks start ◦ Node criticality is measured as node degree. ◦ A node i with degree δ (i) > h attempts to transfer some of its edges to its neighbors. ◦ Δ (i) set of edges delegated by node i cjcj cost of delegating the jth edge in Δ (i) 16

Economic model (ii) New edges are added due to clique formation ◦ Node criticality is measured using path centrality. ◦ A node i with path centrality δ (i) > h is replaced by a clique of size q. 17

Economic model 18

Economic model (ii) New edges are added due to clique formation ◦ Node criticality is measured using path centrality. ◦ A node i with path centrality δ (i) > h is replaced by a clique of size q. CnCn Cost of new nodes forming the clique Δ (i) set of edges delegated by node i cjcj cost of delegating the jth edge in Δ (i) 19

Economic model Defenses and their cost BDBD Maximum budget of defender D C FD Fixed cost of starting a defense round qThe clique size in case delegation is based on cliques C del (h[, q])Cost of implementing delegation for nodes with criticality δ higher than h C cli (q) Cost of replacing each destroyed nodes by a clique consisting of q new nodes. 20

Economic model The cost of clique replacement ◦ A destroyed node is replaced by clique of q nodes. 21

Economic model 22

Economic model The cost of clique replacement ◦ A destroyed node is replaced by clique of q nodes. ◦ CnCn Cost of new nodes forming the clique Δ (i) set of edges delegated by node i cjcj cost of delegating the jth edge in Δ (i) 23

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 24

Measurements LCC(Largest Connected Component) ◦ The reduction in the network connectivity makes communication impossible between some pairs of nodes. ◦ For the attacker: smaller LCC means more successful APL(Average Path Length) ◦ APL increase means communication is still possible, but has become more difficult. ◦ For the attacker: longer APL means more successful 25

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 26

Empirical work SFNG Matlab function which was used to synthesize undirected scale-free network. 4 synthetic networks with 400 nodes each. 1 large real network which is a snapshot of the structure of the Internet at the level of autonomous system taken on July 22, Formed by 22,963 nodes. 27

Empirical work Path centrality computation ◦ Unweighted networks ->Freeman’s betweenness centrality ◦ Weighted networks ->as path centrality the reliability measures 28

Empirical work Weighted networks Undirected Directed (in-reliability) 29 F ij The weight of most reliable path between i and j

Empirical work => Shortest path problem with nonnegative weights => P ij Set of different paths between two nodes i and j WpWp Set of edge weights in path p 30

Empirical work Consider attackers with several levels of partial knowledge on the attacked network: 100%, 80%, 60%, 40%, 20% Conduct 2 simulations(no defense, defense) with each of 4 initial network: Each simulation consisted of 30 attack rounds. 1. unweighted undirected3. weighted undirected 2. unweighted directed4. weighted directed 31

Empirical work For the larger real Internet network, conducted two additional, longer simulation.(with defense, without defense) Each simulation consisted of 1722 attack rounds. Simulation with defense: After a batch of q attack rounds, the defender was allowed to perform one defense round, which replaces the most critical node destroyed in the last q rounds by a clique of q nodes. 32

Empirical work Parameter choice for attack and defense ◦ Threshold criticality h was set in a network- dependent way: only 5% of nodes had criticality δ > h. ◦ Clique size q was oriented by experiments. q = 5. 33

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 34

Discussion of results 1. Unweighted undirected network 35

Discussion of results 2. Unweighted directed network 36

Discussion of results 3. Weighted undirected network 37

Discussion of results 4. Weighted directed network 38

Discussion of results 5. 22,963-node Internet snapshot network 39

Agenda Introduction Economic model Measurements Empirical work Discussion of results Conclusions 40

Conclusions Previous work in this area deals only with un weighted undirected networks and does not clearly say how much attackers and defenders can do. Weights may represent bandwidth, trust, distance, etc. Attacks based on “node degree” or “path centrality”(taking weights into account). Defenses consider “delegation” and “node replacement”. 41

Conclusions Empirical results show that there are no significant differences in the resistance of unweighted and weighted networks. Directed networks were more connected and had more resistance than undirected networks. Regardless of the network type, when the attacker knows only a 20% fraction of the network topology,her attacks are not very harmful. Directed networks which are scale-free can successfully withstand attacks where the attacker knows as much 80% or even 100% of the network topology. 42

Thanks for your Attention ！ Thanks for your Attention ！ 43