1

Particle competition for complex network

community detection Author: Marcos G. Quiles, Liang Zhao,

Ronaldo L. Alonso, and Roseli A.RomeroAn Interdisciplinary Journal of Nonlinear Science

2

The concept-Randomness and Determinism-Competition The method The experiments

Outline

3

Human decision making is a tradoff between randomness and determinism.

When one has complete knowledge about a

specific subject, a deterministic choice can be made, on the other hand, a random decision is made when one knows nothing about it.

Randomness and Determinism

4

Competition is a natural process widely observed in living sharing limited resources.

Competition

5

In the proposed model, particles walk in the network and compete with each other that each of them tries to possess as many nodes as possible.

The process continues until a dynamical equilibrium(when each community has only one particle) state is reached.

The method

6

Each particle has two variables )(,)( tt jvj

j

0)(if,))(()(

0)(if,))(()(

0)(if,)(

)1(

)1(

],[)(

particleofnexploratioofabilitythe

orncompetitiooflevelthezingcharacteripotentialparticletheis:)(

timeatparticlebyvisitedbeingnodethe:)(

min

max

maxmin

jijj

jijj

ij

j

ivj

j

j

j

jivj

tvtt

tvtt

tvt

t

vt

t

t

tvt

7

Each node has three variables iv

momentat this

notor particle aby visitedis node a whether means, iablebinary var a is:

at time node of potential the:)(

state free aat is node if 0or

particle aby occpied if value theit takes

.timeat node theof particleowner theregistersfirst the:)(

ii

ii

jj

ii

vv

tvtv

tvtv

iii vtvtv ,)(,)(

8

jiij

jiivi

ii

i

iij

iii

tvvt

tvvtv

vtv

tv

tvv

vtvtv

)(and1if,)1(

)(and1if,})(,max{

0if,)(

)1(

)(and1if,

0if,)()1(

min

min

9

Each particle has probability pdet to take deterministic moving and 1- pdet to take random moving

Random moving: randomly selects a neighbor to visit(immediately return to the node visited at last iteration is not allowed ,unless the node’s degree is 1).

Deterministic moving: allows the particle always to visit a node that is already owned by it.

10

1

2 3

5 4

67

9

8

11

A particle encounters one of the following three situation s for each visit

1.If a node being visited by a particle has no owner yet.

2.If a node being visited by a particle belong to the particle itself.

3. If a node being visited by a particle belong to another particle.

12

At beginning, K particles are put at K randomly chosen vertices of a network.

Each particle has initial potential

Each node has initial potential

Still at this moment, all vertices are free

j min)0( j

iv min)0( iv

0)0( iv

13

T=0

13

1

2 3

5 4

67

9

8

0)0(2 v

0)0(7 v

21 )0( vv

72 )0( vv

14

The Experiments

15

16