Belaza Vallejo, Andres M

Bramson, Aaron

Casert, Corneel

Hoefman, Kevin

Ryckebusch, Jan

Schoors, Koen

van den Heuvel, Milan

Vandermarliere, Benjamin

Ghent University Academic Bibliography

Introduction Methods Results ConclusionsQuantifying the Role of Inactive Links in SocialNetworksAndres M. Belaza Jan Ryckebusch et al.Ghent Universityandres.belaza@ugent.beThe 7th International Conference onComplex Networks and Their ApplicationsCambridge, United Kingdom2018, Dec 13Introduction Methods Results ConclusionsOverviewIntroductionPolitical NetworksSocial BalanceMethodsStatistical Physics - An Energy-based ApproximationApplicationsResultsTransition ProbabilitiesRelation between Global Network MeasuresConclusionsIntroduction Methods Results ConclusionsPolitical Networks1960 Alliances and Disputes network of countries.Introduction Methods Results Conclusions“Social Balance”: emergent properties in the network ofrelationshipsBalanced triads:• “A friend of a friend is alsoa friend.”• “An enemy of my enemy ismy friend.”Problem: sometimes theunbalanced (or frustrated)triangles are common.Introduction Methods Results ConclusionsVirtual worlds and the real worldDatasets forpolitical networks:Real World• International relationships during theCold War (CW) era (1949-1993).• Extracted from the Correlates of Wardatabase.Virtual World• From EVE Online: an MMORPG.• Alliances raise taxes and controlterritory: player-created alliances play arole similar to that of a state.• Diplomatic relationships betweenalliances of players from March 2015 toApril 2016.• Two networks: “Big alliances” (+200members) and “Alliances withsovereignty” (SOV).Introduction Methods Results ConclusionsBalance: real network versus random networkIn EVE Online• Balanced triads [+−−] (red)and [+ + +] (magenta) aremore common than random.• Strongly frustrated triads[+ +−] (blue) are much lesscommon than random.• Lowly unbalanced triads[−−−] (green) are slightlymore common than random.• Emergent features: hierarchybetween triads is persistentover time and across networks.Occupation probabilities for fourtypes of triads for the relationshipsbetween the alliances in EVE OnlineIntroduction Methods Results ConclusionsThe occurrence of inactive links in political networks• Three-nodecycles withactive edgestypicallyrepresent a fewpercent of allpossible triads inthe politicalnetworks.• The bulk of thetriads involveinactive edges.• Informationcontained in theinactive edges?What is the effect of inactive (neutral ornonexistent) edges in political networks?Introduction Methods Results ConclusionsHamiltonian approach to extended social balance• Energy ∼ occupation probability (population of lower-energystates is higher)• Adding inactive edges: edge attribute sij = {−1, 0,+1}• Hamiltonian for the generative mechanisms in the networkH ({sij}) = 16N∑i 6=j 6=k=1[− α sijsiksjk︸ ︷︷ ︸three-edge interaction− γ (sijsik + sijsjk + sjksik)︸ ︷︷ ︸two-edge interaction]+12N∑i 6=j=1[+ω sij︸ ︷︷ ︸one-edge interaction+ µ s2ij︸ ︷︷ ︸chemical potential],Two applications (predictive power):1. Average sign of a link (L) and the fraction of active links (A)2. Transition probabilities between different triadic statesIntroduction Methods Results ConclusionsMean-field approach to the proposed HamiltonianUsing a mean-field approximation and the global networkproperties:• Magnetization L ≡ 〈sij〉 (−1 ≤ L ≤ +1)• Activation A ≡〈s2ij〉(0 ≤ A ≤ +1)• Non-trivial relationship between network properties (datacollapse?)GMF (L,A) ≡arctanh(−LA)ln([1A − 1]2cosh[arctanh(−LA)])≈ ωµ− 2γ3µ(N − 2)L .Introduction Methods Results ConclusionsMeasuring transition probabilities between triadic statesThe transitionprobabilities betweenthe triadic states σ andσ′:P(σ → σ′) ∝exp−β (Eσ′ − Eσ)Energy decreasingtransitions are morecommon than energyincreasing ones.Example of transition probabilities(consecutive days) between triadic statesfor alliances in EVE Online.Introduction Methods Results ConclusionsPredicting transition probabilities between triadic statesThe transitions are consistent with the energy differences.In units of the standard deviation, differences between thepredicted and measured transition probability.Introduction Methods Results ConclusionsRelation between global network measuresGMF (L,A) ≡arctanh(−LA)ln([1A − 1]2cosh[arctanh(−LA)]) ≈ ωµ− 2γ3µ(N − 2)L-20 -10 0 10L(N−2)-0.2-0.10.00.1MF(L,A)Cold WarEVE(SOV)EVE(+200)LA◦ L:magnetization(average signof a link)◦ A:activation(fraction ofactive links)Introduction Methods Results ConclusionsConclusions• Inactive edges in political networks are a source of information.• Selected properties of relationships in political networks areremarkably constant across time and networks.• A Hamiltonian approach to social balance is proposed.• The proposed model has predictive power and can uncovergenerative mechanisms1. The activation of links can be related to an ”activationenergy”.2. The transition probabilities in our data are consistent with thedifferences in energies.3. The mean-field approximation allows one to define andcalculate the systems magnetization (L) and average activation(A)..jpgIntroduction Methods Results ConclusionsThanks• Belaza, Andres M. et. al. (2017)Statistical physics of balance theoryPLOSOne 12(8): e0183696 .• Belaza, Andres M. et. al. (2018)Social Stability and Extended Social Balance -Quantifying the Role of Inactive Links in Social NetworksarXiv:1807.09042Email: andres.belaza@ugent.be

Quantifying the role of inactive links in social networks

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Quantifying the role of inactive links in social networks

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