Co-evolution of network structure and content

Lada Adamic

School of Information & Center for the Study of Complex Systems

University of Michigan

Outline

Co-evolution of network structure and content Can the structure of Twitter and virtual world interactions

reveal something about their content? http://arxiv.org/abs/1107.5543

Can the structure of a commodity futures trading network reveal something about information flowing into the market? http://papers.ssrn.com/sol3/papers.cfm?

abstract_id=1361184

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What is the relationship between network structure and information diffusion?

Is information flowing over the network?Or is information shaping the network?

Can the shape of the network reveal properties of information

Big news! Giant microbes!

Can the shape of the network reveal properties of information

Little news. How’s the weather?

Related work on time evolving graphs

Densification over time (Leskovec et al. 2005)

Community structure over time (Leicht et al. 2007, Mucha et al. 2010)

Change in structure (ability to “compress” network) signals events (Graphscope by Sun et al. 2007)

Disease propagation & timing (Moody 2002, Liljeros 2010)

Enron email (B. Aven, 2011)

What’s different here

We look at network dynamics at relatively short time scales and construct time series

A range of network metrics, instead of just community structure

Information novelty and diversity as opposed to tracking single events / pieces of information

Can the network reveal… If everyone is talking about the same thing, or if there is

just background chatter.

If what they are talking about is novel?

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1st context: virtual worlds

Networks: asset transfers (gestures, landmarks) and transactions (e.g. rent, object purchases)

Content: assets being transferred

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Study transfers in the context of 100 groups with highest numbers of transfers

Second context: Twitter Network microblogging : < 140 characters / tweet

Network links read from tweets Reply or mention: by putting the @ in

front of the username

Retweet: repeat something someone else wrote on twitter, preceded by the letters RT and @ in front of their username

Selecting Twitter communities to track

http://wefollow.com/twitter/researcher

For each “researcher” gather tweets of accounts they follow

Highly dynamic networks

Segmentation: Twitter: every 800

tweets median segment

duration 1.5 days SecondLife: every

50 asset transfers median segment

duration 8.4 days

% o

f edges

repeate

d

Segments elapsed

Conductance:capturing potential for information flow

A B A B

A B

low conductance

medium conductance

high conductance

Temporal conductance (summed over all pairs): High if pairs of nodes share edges, or many short,

indirect paths

Koren, North, Volinsky, KDD, 2006

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Network expectedness

Define expectedness: Average conductance of all neighbor pairs at time t, based on conductance of pair at time t-1

expected

unexpected

Conductance and expectedness as a toy network evolves

a

b

c

d

a

b

c

a

b

c

a

b

c

network configuration at t = 0

possible configurations at t = 1

conductance = 4

conductance = 4expectedness = 1.5edge jaccard = 1

conductance = 4.5expectedness = 1.3333edge jaccard = 0.6667

conductance = 6expectedness = 0.5edge jaccard = 0.25

SecondLife: network structure and content

overlapt,t+1

overlap t-1,t

D diversityt, (t+1)

standard network metrics are not indicative of information properties

conductance and expectedness are

D diversityt-1, t

Conductance & diversity of information

High conductance brings higher content diversity

Repeat network patterns bring less diversity and less novelty

but… similarity and novelty are positively correlated (r = 0.19)

Social and transaction network of top sellers in SL

Twitter: textual diversity and novelty

Semantic metrics

Metric Type Computation Methods

Contemporary Metrics

(average cosine similarity of words in

Tweets)

between connected node pairs in the graph

between indirectly-connected node pairs, i.e., non-neighbors with an undirected path of length > 1 between them

between isolated pairs (in different components)

Novelty Metric(Language Model

distance)

between two sets of tweets associated with Twitter networks captured at different times

Twitter: network structure and information diversity

netw

ork

str

uct

ure

content similarity

Inferring Network Semantic Information

Question: Does the network structural information help to improve the prediction performance of the characteristics of information exchanged?

Kernel Regression Prediction

Model

Semantic variables

Topological variables

Semantic variables

Example: Inferring the average similarity score between isolated pairs

Don’t need to use other textual variables (e.g. similarity between indirectly connected pairs) when sufficient topological information available

Reason: topological variables account for much of the pattern in the text!

The input variables of curve ci start from

Xi and increase each time by adding the variable labeled on x-axis.

Network structure and information novelty

Greater novelty in edges corresponds to greater novelty in content shared

For nodes that are interacting (citing or being cited): Higher

conductance and expectedness correlates with less information novelty

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Information in trading networks

CFTC = Commodity futures trading commission

stated mission: protect market users and the public from fraud, manipulation, and abusive practices

futures contracts started out as contracts for agricultural products, but expanded to more exotic contracts, including index futures

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1361184

Collaboration with Celso Brunetti, Jeff Harris, and Andrei Kirilenko

Data

6.3 million transactions in Aug. 2008 in the Sept. E-mini S&P futures contract

price discovery for the index occurs mostly in this contract (Hasbrouck (2003))

data includes: date & time, executing broker, opposite broker, buy or sell, price, quantity

sample in transaction windows of 240 transactionsexecuting broker opposite broker

quantity: 10price: $171.25

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matching algorithm

limit order book

buy 30 contracts at $171.25sell 10 contracts at $171.25

sell 20 contracts at $172.00

sell 5 contracts at $171.75 buy 20 contracts at $171.50

buy 50 contracts at $171.00

buy 30 contracts at $171.25

buy 20 contracts at $171.50

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not social, not intentional, not persistent

Financial variables

Rate of return: Last price to first price in logs (close-to-open)

Volatility: Range – log difference between max and min price

Duration: Total period duration - time in seconds between the start and end of each sampling period

Proxy for arrival of new information

Volume: Trading volume – number of contracts traded

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What can we learn from network structure?e.g. centralization?

low in-centralization high in-centralization

low indegree

high indegreehigh outdegree

low outdegree

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overview of network variables

# nodes, # edges

clustering coefficient, LSCC, reciprocity

CEN = giniin-degree – giniout-degree

INOUT = r(indegree of node, outdegree of same node)

AI (asymmetric information)

Correlations between network and financial variables

High Centralization: market dominance - a dominant trader buys from many small sellers – low duration, low volume

Negative assortativity: large sellers sell to small buyers and vice versa – low duration, higher volume

Correlations between network and financial variables

High av. degree & largest strongly connected component: no news - many buyers and sellers – high duration, high volume

Correlations between network and financial variables

Correlations between network and financial variables

Rate of return: positive correlation with centralization

Volatility & duration: correlated with standard deviation of degree, average deg. and the total number of edges (E).

Volume: Correlated with a few network variables, sign varies.

Conclusion Network structure alone is revealing of the diversity and

novelty information content being transmitted

Results depend on the scope and relative position of the activity in the network

Future work Sensitivity to inclusion of non-interactive or across-community

interactions

Applying novelty & conductance metrics to financial time series

Continuous formulation of novelty and other network metrics (because segmentation is problematic)

Roles of individual nodes

Thanks:

Edwin Teng Liuling Gong Avishay Livne

Information network academic research centerINARC

Questions?