PhD thesis defense

1. Evolutionary Dynamics on Evolving Graphs -4 -3 -2 -1 0 1 2 3 Barbara Ikica Faculty of Mathematics and Physics University of Ljubljana 18 December 2019

2. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs

10. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs Players/agents P = , , , , ,

11. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs Players/agents P = , , , , , Strategies/states Si = , ,

12. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs Players/agents P = , , , , , Strategies/states Si = , , Payoﬀ πi : , , , , , →

13. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs Players/agents P = , , , , , Strategies/states Si = , , Payoﬀ πi : , , , , , → Update rule pi→j = 1 + e−ω[πi−πj] −1 (Fermi rule)

26. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs tD tG := time scale of the dynamics graph

27. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs tD tG := time scale of the dynamics graph tD tG

28. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs tD tG := time scale of the dynamics graph tD tG tD tG

29. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Evolutionary Dynamics on Evolving Graphs tD tG := time scale of the dynamics graph tD tG tD tG tD ∼ tG

30. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow tD tG

31. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow tD tG

32. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow tD ∼ tG NEWSLOREM IPSUM DOLORSITAMET No. 11:12:2014 LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSIT AMET LOREM IPSUM DOLORSIT AMET LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET UMMM LORELORE LORELORELORELORELORELOREM IPM IPM IPM IPSUMSUMSUMSUM DOLO LORELORELOREM IPM IPM IPM IPSUMSUMSUMSUMSUMSUM DOLODOLODOLODOLODOLODOLODOLODOLOR SIR SIR SIR SIR SIT AMT AM LOREM IPM IPM IPSUMSUMSUM DOLODOLODOLOR SIR SIR SIR SIR SIR SIT AMT AMT AMT AMT AMT AMT AMT AMETETETETET LORELORELORELOREM IP DOLORSIRSIRSITAMTAMTAMTAMETET LORELOREM IPM IP LORELOREM IPM IPSUM DOLO AMETAMETLORELORELOREM IPM IPM IPSUMSUM DOLOR SIT AM IPSUM DOM DOLORLORLORSITSITSIT AMETAMETAMET LOLOREMREMREM IPSU LLLO DO NEWSLOREM IPSUM DOLOR SITAMET No. 11:12:2014 LOREMIPSUMDOLORSITAMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMIPSUMDOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET

33. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow tD ∼ tG NEWSLOREM IPSUM DOLORSITAMET No. 11:12:2014 LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSIT AMET LOREM IPSUM DOLORSIT AMET LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET UMMM LORELORE LORELORELORELORELORELOREM IPM IPM IPM IPSUMSUMSUMSUM DOLO LORELORELOREM IPM IPM IPM IPSUMSUMSUMSUMSUMSUM DOLODOLODOLODOLODOLODOLODOLODOLOR SIR SIR SIR SIR SIT AMT AM LOREM IPM IPM IPSUMSUMSUM DOLODOLODOLOR SIR SIR SIR SIR SIR SIT AMT AMT AMT AMT AMT AMT AMT AMETETETETET LORELORELORELOREM IP DOLORSIRSIRSITAMTAMTAMTAMETET LORELOREM IPM IP LORELOREM IPM IPSUM DOLO AMETAMETLORELORELOREM IPM IPM IPSUMSUM DOLOR SIT AM IPSUM DOM DOLORLORLORSITSITSIT AMETAMETAMET LOLOREMREMREM IPSU LLLO DO NEWSLOREM IPSUM DOLOR SITAMET No. 11:12:2014 LOREMIPSUMDOLORSITAMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMIPSUMDOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET News providers

34. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow tD ∼ tG NEWSLOREM IPSUM DOLORSITAMET No. 11:12:2014 LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSIT AMET LOREM IPSUM DOLORSIT AMET LOREMIPSUM DOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLORSITAMET UMMM LORELORE LORELORELORELORELORELOREM IPM IPM IPM IPSUMSUMSUMSUM DOLO LORELORELOREM IPM IPM IPM IPSUMSUMSUMSUMSUMSUM DOLODOLODOLODOLODOLODOLODOLODOLOR SIR SIR SIR SIR SIT AMT AM LOREM IPM IPM IPSUMSUMSUM DOLODOLODOLOR SIR SIR SIR SIR SIR SIT AMT AMT AMT AMT AMT AMT AMT AMETETETETET LORELORELORELOREM IP DOLORSIRSIRSITAMTAMTAMTAMETET LORELOREM IPM IP LORELOREM IPM IPSUM DOLO AMETAMETLORELORELOREM IPM IPM IPSUMSUM DOLOR SIT AM IPSUM DOM DOLORLORLORSITSITSIT AMETAMETAMET LOLOREMREMREM IPSU LLLO DO NEWSLOREM IPSUM DOLOR SITAMET No. 11:12:2014 LOREMIPSUMDOLORSITAMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMT LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMETLOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREMIPSUMDOLORSITAMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SIT AMET LOREM IPSUM DOLOR SITAMET News providers News consumers

45. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Outline I Evolutionary Dynamics on Graphs (tD tG)

46. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Outline I Evolutionary Dynamics on Graphs (tD tG) • The Modiﬁed Petford–Welsh Algorithm

47. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Outline I Evolutionary Dynamics on Graphs (tD tG) • The Modiﬁed Petford–Welsh Algorithm II Evolving Graphs (tD ∼ tG)

48. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow Outline I Evolutionary Dynamics on Graphs (tD tG) • The Modiﬁed Petford–Welsh Algorithm II Evolving Graphs (tD ∼ tG) • Co-evolution of the Multilayer News Flow

49. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm

50. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Petford–Welsh algorithm Petford, A. D. & Welsh, D. J. A. A Randomised 3-Colouring Algorithm, Discrete Math. 74 (1989), 253–261.

51. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Petford–Welsh algorithm Petford, A. D. & Welsh, D. J. A. A Randomised 3-Colouring Algorithm, Discrete Math. 74 (1989), 253–261. Žerovnik, J. A Randomized Algorithm for k-Colorability, Discrete Math. 131 (1994), 379–393.

53. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A proper colouring is an assignment of colours to the vertices of a graph so that no two adjacent vertices have the same colour, i.e., c : V → {1, 2, . . . , k} s.t. c(i) = c(j) for all ij ∈ E.

56. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A proper colouring is an assignment of colours to the vertices of a graph so that no two adjacent vertices have the same colour, i.e., c : V → {1, 2, . . . , k} s.t. c(i) = c(j) for all ij ∈ E. A graph that has a k-colouring is said to be k-colourable.

57. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A proper colouring is an assignment of colours to the vertices of a graph so that no two adjacent vertices have the same colour, i.e., c : V → {1, 2, . . . , k} s.t. c(i) = c(j) for all ij ∈ E. A graph that has a k-colouring is said to be k-colourable.

59. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm

60. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring

61. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring

62. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring 2. while (there is a bad vertex) and (not too many steps) repeat

65. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring 2. while (there is a bad vertex) and (not too many steps) repeat 2.1 choose a bad vertex v uniformly at random

66. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring 2. while (there is a bad vertex) and (not too many steps) repeat 2.1 choose a bad vertex v uniformly at random

67. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring 2. while (there is a bad vertex) and (not too many steps) repeat 2.1 choose a bad vertex v uniformly at random 2.2 choose a new colour i for v proportionally to ω−N (v,i), ω > 1

68. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised k-colouring algorithm 1. generate an initial k-colouring 2. while (there is a bad vertex) and (not too many steps) repeat 2.1 choose a bad vertex v uniformly at random 2.2 choose a new colour i for v proportionally to ω−N (v,i), ω > 1 N , r = 1 N , b = 2 N , y = 0

78. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable.

79. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable. ω −N ,

80. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable. • ... is akin to the Glauber dynamics of the Ising model. ω −N ,

81. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable. • ... is akin to the Glauber dynamics of the Ising model. ω +N ,

82. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable. • ... is akin to the Glauber dynamics of the Ising model. ω +N , 1 + e∆E/(kBT ) −1

83. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The Petford–Welsh algorithm ... • ... acts locally; thus, it is highly parallelisable. • ... is akin to the Glauber dynamics of the Ising model. ω +N , 1 + e∆E/(kBT ) −1

85. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Graph colouring

87. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Graph clustering

88. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Graph clustering [partitioning or grouping data into similar subsets]

89. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Graph clustering [partitioning or grouping data into similar subsets]

90. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The goal of clustering is to separate a given set of objects X = {x1, x2, . . . , xn} into non-overlapping groups/clusters C = {C1, C2, . . . , Cm} that satisfy

93. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The goal of clustering is to separate a given set of objects X = {x1, x2, . . . , xn} into non-overlapping groups/clusters C = {C1, C2, . . . , Cm} that satisfy Ci = ∅ for all 1 ≤ i ≤ m,

94. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The goal of clustering is to separate a given set of objects X = {x1, x2, . . . , xn} into non-overlapping groups/clusters C = {C1, C2, . . . , Cm} that satisfy Ci = ∅ for all 1 ≤ i ≤ m, Ci ∩ Cj = ∅ for all 1 ≤ i < j ≤ m,

95. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm The goal of clustering is to separate a given set of objects X = {x1, x2, . . . , xn} into non-overlapping groups/clusters C = {C1, C2, . . . , Cm} that satisfy Ci = ∅ for all 1 ≤ i ≤ m, Ci ∩ Cj = ∅ for all 1 ≤ i < j ≤ m, m i=1 Ci = X .

96. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW]

97. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering

98. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering

99. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering 2. while (there is a bad vertex) and (Var [bad edges] ≥ tol) repeat

100. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering 2. while (there is a bad vertex) and (Var [bad edges] ≥ tol) repeat

101. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering 2. while (there is a bad vertex) and (Var [bad edges] ≥ tol) repeat 2.1 choose a bad vertex v uniformly at random

102. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering 2. while (there is a bad vertex) and (Var [bad edges] ≥ tol) repeat 2.1 choose a bad vertex v uniformly at random

103. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm A randomised clustering algorithm [https://github.com/ikicab/mPW] 1. generate an initial k-clustering 2. while (there is a bad vertex) and (Var [bad edges] ≥ tol) repeat 2.1 choose a bad vertex v uniformly at random 2.2 choose a new colour i for v proportionally to ω+N(v, i), ω > 1

117. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition Varstep = Var (bad edges [1 : step]) < tol

118. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition Varstep = Var (bad edges[step − L + 1 : step]) < tol

119. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition bad edges = [] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

120. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = 1 : bad edges = [b1] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

121. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = 1 : bad edges = [b1] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

122. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = 2 : bad edges = [b1, b2] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

123. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = L : bad edges = [b1, b2, . . . , bL] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

126. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = L + 1 : bad edges = [b1, b2, . . . , bL, bL+1] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L

127. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = L + 1 : bad edges = [b1, b2, . . . , bL, bL+1] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L µL+1 = µL + 1 L (bL+1 − b1)

128. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = L + 1 : bad edges = [b1, b2, . . . , bL, bL+1] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L µL+1 = µL + 1 L (bL+1 − b1) VarL+1 = VarL + 1 L − 1 (bL+1 − b1)(bL+1 + b1 − µL+1 − µL)

129. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Stopping Condition step = L + 2 : bad edges = [b1, b2, . . . , bL, bL+1, bL+2] µL = 1 L (b1 + b2 + . . . + bL) VarL = 1 L − 1 b2 1 + b2 2 + . . . + b2 L − L L − 1 µ2 L µL+2 = µL+1 + 1 L (bL+2 − b2) VarL+2 = VarL+1 + 1 L − 1 (bL+2 − b2)(bL+2 + b2 − µL+2 − µL+1)

130. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Fine-tuning Problems

131. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modified Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modified Petford–Welsh Algorithm Fine-tuning Problems • different clusters get assigned the same colour due to random seeds

137. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modified Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modified Petford–Welsh Algorithm Fine-tuning Problems • different clusters get assigned the same colour due to random seeds • outliers (singleton clusters)

142. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Experiments Zachary (|V | = 34, |E| = 78) Ties among the members of a university karate club by Wayne Zachary.

143. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Experiments Zachary (|V | = 34, |E| = 78) Ties among the members of a university karate club by Wayne Zachary. Method NMI ARI φ γ Q |C| Edge betweenness 0.517 0.392 0.424 0.692 0.401 5 Fastgreedy 0.576 0.568 0.574 0.756 0.381 3 Infomap 0.578 0.591 0.668 0.821 0.402 3 Label propagation 0.865 0.882 0.773 0.949 0.415 3 Leading eigenvector 0.612 0.435 0.487 0.667 0.393 4 Multilevel 0.516 0.392 0.558 0.731 0.419 4 Spinglass 0.627 0.509 0.563 0.756 0.420 4 Walktrap 0.531 0.321 0.434 0.590 0.353 5 mPW 1.000 1.000 0.773 0.949 0.403 2

144. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Experiments International E-road network (|V | = 1040, |E| = 1305) tol = 0.001 An international system for numbering and designating roads stretching throughout Europe and some parts of Central Asia.

145. Evolutionary Dynamics on Evolving Graphs Barbara Ikica Motivation Outline Evolutionary Dynamics on Graphs The Modiﬁed Petford–Welsh Algorithm Evolving Graphs Co-evolution of the Multilayer News Flow The Modiﬁed Petford–Welsh Algorithm Experiments International E-road network (|V | = 1040, |E| = 1305) tol = 0.0007 An international system for numbering and designating roads stretching throughout Europe and some parts of Central Asia.

PhD thesis defense

Recommended

Recommended

More Related Content

Recently uploaded

Recently uploaded (20)

Featured

Featured (20)

PhD thesis defense