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

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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)

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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:

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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

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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