Mobile Communication N etworks
description
Transcript of Mobile Communication N etworks
Mobile Communication Networks
Vahid MirjaliliDepartment of Mechanical Engineering
Department of Biochemistry & Molecular Biology
Understanding Social Networks
• Examine the communication pattern of million mobile phone users
• Social networks are robust to the removal of strong ties, but fall apart if the weak ties are removed
• 18 weeks of all mobile call records, 90% of the population of the country use mobile phones
• A single call between 2 individuals during 18 weeks is ignored
• Reciprocal calls with long durations are considered as some type of relationship (family, leisure, ..)
Building the Mobile Call Graph (MCG)• An undirected link between A & B if there is at least
one reciprocal call between them• The weights: • A large number of single calls are removed
• The MCG: • 84.1% of the graph belong to a single connected
cluster (giant component)• Time for sampling? – little difference between sampling 2- or 3-months
BAbetweendurationcallaggregated BAAB ww
6106.4 N 6100.7 L
MCG results:
Degree distribution:Number of links per node
Most of the people only interact with a few
Only a few communicate with more than 10 people Fitted with exponential curve
(strong decay)
Link weight distribution:
The majority only have short communication time
A few have long conversations
Overlap between 2 nodes:
• The overlap between two nodes: the ratio of their shared nodes to their total connected nodes
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3- hypothesses governing the social networks
1. Global Efficiency Principle– Complex networks organize themselves in a way that the tie strengths
maximize the overall flow in the network– Correlation between the weight of a link and its betweenness centrality
(the number of shortest paths of all pairs of nodes passing through it)2. Dyadic hypothesis
– The strength of a link only depends on the nature of the relationship between the individuals
– Tie strength is independent of the network surrounding it3. Strength of weak tie hypothesis– The strength of a tie between A and B increases as the overlap
between their friendship circles increases
The network around a randomly selected node (up to 6 levels)
Link color shows tie strength
Majority of strong ties are found within clusters (intra-cluster links vs. inter-cluster)
Inter-community links are usually weaker
In contract to a real network
• A dyadic network, generated by randomly permuting the ties in the previous one
=> dyadic hypothesis
• The weights are derived based on the links betweenness centrality ijb
• The links connecting different communities have high (red)
but the links inside a community have low (green)
ijb
ijb
Tie strength & network structure• Removing weak / strong ties:• The size of giant component: – The fraction of nodes that can all reach other as a
function of the fraction of removed links •
• Network disintegration: – Based on ties’ strength: – Based on overlap:
)( fRgc
f
8.0wf
6.0Of
max
/~ 2
sss NSnS nodes s withclusters ofnumber :sn
Removing linksBased on weights Based on overlap
Red: removing the weakest ties Black: removing the strongest ties
• Percolation theory: – divergence occurs as we approach the critical
threshold – phase transition
• Removing the weak ties first, shows a divergence
• No divergence observed if removing the strong ties first
max
/~ 2
sss NSnS
Contrast between Social Networks vs Biological Networks
• Biological networks: strong ties play more important roles than weak ties
• Social networks: strong ties are inter-community links, and removing strong ties will disconnect the small communities from each other, but the global network will NOT collapse
Information Diffusion
• Monitoring the information spread starting from a randomly selected individual with some novel information
• Probability of passing the information:
rate spreading overal:xwxP ijij
• For the control run, the average of all the weights is used
Control : all ties are considered equalReal : considering the real network with real weights
trapped
Information gets trapped inside a community before leaving for a new community
• Distribution of the strength of a tie responsible for the first infection of a node
Real network: peak at w=100 (intermediate strength)
control: information spread is independent of tie strength (weak ties inside a community are responsible for the information spread)
Overall direction of information flow
Number of times information is passed in the given direction
Total number of transmission from the link
• In the control runs, the information flows through the shortest paths
• In the real network: the information is passed through a strong tie backbone, and the regions connected to it– Half of the network is rarely affected (lower part
of the real simulation)
Conclusion:
• Unexpected result: removal of weak ties can collapse the social network, while other networks are mainly fragile to the removal if string ties
• Information trapping in small communities observed
• The information is mostly passed through intermediate ties