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?   Can the structure of a commodity futures trading network reveal something about information flowing into the market? 

3 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 (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?

1 st context: virtual worlds  Networks: asset transfers (gestures, landmarks) and transactions (e.g. rent, object purchases)  Content: assets being transferred 10

Study transfers in the context of 100 groups with highest numbers of transfers 11

Second context: Twitter Network  microblogging : < 140 characters / tweet  Network links read from tweets  Reply or mention: by putting in front of the username  Retweet : repeat something someone else wrote on twitter, preceded by the letters RT in front of their username

Selecting Twitter communities to track   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 % of edges repeated 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

Network expectedness  Define expectedness:  Average conductance of all neighbor pairs at time t,  based on conductance of pair at time t-1 16 expected unexpected

Conductan ce and expectedn ess as a toy network evolves d network configuratio n at t = 0 possible configuratio ns at t = 1 conductance = 4 expectedness = 1.5 edge jaccard = 1 conductance = 4.5 expectedness = edge jaccard = conductance = 6 expectedness = 0.5 edge jaccard = 0.25

SecondLife: network structure and content overlap t,t+1 overlap t-1,t  diversity t, (t+1) standard network metrics are not indicative of information properties conductance and expectedness are  diversity t-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 (  = 0.19) Social and transaction network of top sellers in SL

Twitter: textual diversity and novelty  Semantic metrics Metric TypeComputation 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 network structure 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 c i start from X i 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

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 Collaboration with Celso Brunetti, Jeff Harris, and Andrei Kirilenko

Data  6.3 million transactions in Aug 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 transactions executing brokeropposite broker quantity: 10 price: $171.25

matching algorithm  limit order book 27 buy 30 contracts at $ sell 10 contracts at $ sell 20 contracts at $ sell 5 contracts at $ buy 20 contracts at $ buy 50 contracts at $ buy 30 contracts at $ buy 20 contracts at $171.50

not social, not intentional, not persistent 28

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

What can we learn from network structure? e.g. centralization? low in-centralizationhigh in-centralization 30 low indegree high indegree high outdegree low outdegree

overview of network variables  # nodes, # edges  clustering coefficient, LSCC, reciprocity  CEN = gini in-degree – gini out-degree  INOUT =  (indegree of node, outdegree of same node)  AI (asymmetric information) 31

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

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 center

Questions?