Network analysis of complex systems Peter Andras School of Computing Science Newcastle University 22 Overview Network analysis background Network analysis background Brain area networks Brain area networks Protein interaction systems Protein interaction systems Ecological system Ecological system Organisations Organisations Large-scale software systems Large-scale software systems 33 Networks Molecular interaction networks Molecular interaction networks Cellular interaction networks Cellular interaction networks Human interaction networks Human interaction networks Software interaction networks Software interaction networks 44 Erdos-Renyi vs Scale-free networks Erdos-Renyi networks: uniform probability of links between any two nodes exponential distribution of connectedness (P(k)=exp(- *k)) very few highly connected nodes Erdos-Renyi networks: uniform probability of links between any two nodes exponential distribution of connectedness (P(k)=exp(- *k)) very few highly connected nodes Scale-free networks: more connected nodes are more likely to be linked to other nodes power law distribution of connectedness (P(k)=k^(- )) some very highly connected nodes Scale-free networks: more connected nodes are more likely to be linked to other nodes power law distribution of connectedness (P(k)=k^(- )) some very highly connected nodes 55 Real networks Many real networks (biological, social, technological) are scale-free networks Many real networks (biological, social, technological) are scale-free networks E.g. networks of brain areas are more similar to scale-free networks than to Erdos-Renyi networks (Kaiser et al, 2007) E.g. networks of brain areas are more similar to scale-free networks than to Erdos-Renyi networks (Kaiser et al, 2007) 66 Implications of being scale-free Scale-free networks are robust to random damage, but vulnerable to well- targeted damage Scale-free networks are robust to random damage, but vulnerable to well- targeted damage Scale-free networks grow through preferential attachment Scale-free networks grow through preferential attachment Brain area networks CoCoMac database connectivity of brain areas in cat and macaque (brain areas defined in histological sense) CoCoMac database connectivity of brain areas in cat and macaque (brain areas defined in histological sense) Connectivity ~ estimate of the number / relative importance of connecting axons Connectivity ~ estimate of the number / relative importance of connecting axons E.g. V1 receives around 5% of its inputs from LGN E.g. V1 receives around 5% of its inputs from LGN 7 Are these networks scale-free ? Networks: around 60 nodes with 600 800 connections small networks Networks: around 60 nodes with 600 800 connections small networks Measurements of such small size networks may be misleading Measurements of such small size networks may be misleading 8 (Kaiser et al, 2007) Comparison of networks Method: Method: measure key parameters of these networks (average clustering coefficient and average connectivity) measure key parameters of these networks (average clustering coefficient and average connectivity) generate a set of scale-free networks and a set of exponential networks with the same parameters generate a set of scale-free networks and a set of exponential networks with the same parameters test statistically whether the brain networks behave in the same way or not in terms of damage measures as the random sample of scale- free or exponential networks test both random and targeted damage test statistically whether the brain networks behave in the same way or not in terms of damage measures as the random sample of scale- free or exponential networks test both random and targeted damage 9 Determination of scale-free-ness The analysis shows that the brain networks are more similar to scale-free networks than to exponential networks The analysis shows that the brain networks are more similar to scale-free networks than to exponential networks However, in terms of the evolution of the average clustering coefficient under targeted node elimination the brain networks are more similar to exponential networks However, in terms of the evolution of the average clustering coefficient under targeted node elimination the brain networks are more similar to exponential networks 10 Macaque brain network with random and targeted node elimination 11 Protein interactions networks Aim: kill bacteria 12 Important nodes Importance contribution to structural network integrity Importance contribution to structural network integrity Key assumption: structural and functional integrity correlates well (e.g. 80% of proteins corresponding to structurally nodes in B. subtilis are essential Idowu & Andras, 2005) Key assumption: structural and functional integrity correlates well (e.g. 80% of proteins corresponding to structurally nodes in B. subtilis are essential Idowu & Andras, 2005) Centrality measures: Centrality measures: Connectedness Hubs Connectedness Hubs Betweenness Bottlenecks Betweenness Bottlenecks 13 Measuring damage Integrity measures: Integrity measures: Average shortest path length Average shortest path length Average clustering coefficient Average clustering coefficient Number of isolated sub-networks Number of isolated sub-networks Calculation of benchmark damage average values of integrity measures after n% of randomly selected nodes are removed Calculation of benchmark damage average values of integrity measures after n% of randomly selected nodes are removed Damage effect measured as equivalent average random damage comparability Damage effect measured as equivalent average random damage comparability (Idowu and Andras, 2005; Idowu et al, 2004) 14 Searching for drug targets Parasite and host proteomes Parasite and host proteomes Network analysis to reveal important nodes (hubs and bottlenecks) Network analysis to reveal important nodes (hubs and bottlenecks) Filtering against host proteins Filtering against host proteins Combinatorial optimisation using the equivalent damage measures Combinatorial optimisation using the equivalent damage measures Result: pairs and triples of potential targets Result: pairs and triples of potential targets Note: most single targets are already known Note: most single targets are already known (EU & US Patents e-Therapeutics Plc / Newcastle University) 15 Ecological system Winter wheat field Food-web network of plant and animal species complemented by natural physical factors (sunlight, wind, soil type), diseases (viruses, bacteria, fungi) Human intervention pesticides How to avoid damaging the ecological system too much, while protecting the crop ? 16 Network of species and other factors Data from the Boxworth project (1992) 184 nodes in the network: 118 species, 43 diseases, 23 other factors 82 pesticides with 61 active ingredients Weighted links to represent supporting and damaging interactions (asymmetric graph) Four seasons separate networks (Andras et al, 2007) 17 Ecological network analysis System integrity integrity measures Average shortest path length Clustering coefficient Benchmark curves of variation of integrity damage using averaged damage effect calculated for randomly selected sets of nodes (same size sets e.g. 1 node, 2 nodes, etc.) together with corresponding damage variances 18 Damage evaluation Consider a pesticide or combination of pesticides Remove affected nodes and their links from the network, further remove nodes and links which lack enough supporting links Calculate integrity measures and assess the equivalent random damage by statistical testing of identity of calculated damage and the average benchmark damage 19 Pesticide application optimisation Consider pesticide combinations that are expected to be functionally equivalent from the perspective of crop protection Calculate the effect of considered pesticide combinations for the whole year for the four seasonal system graphs Choose the combination that causes minimal expected damage Organisations 1 Humans working together to deliver goods and services Humans working together to deliver goods and services Organisational hierarchy: units, management Organisational hierarchy: units, management 20 Organisations 2 Network of human interactions Network of human interactions Humans act as communication units Humans act as communication units The organisation is the dynamic network of interrelated human communications that follow a set of organisation-specific rules The organisation is the dynamic network of interrelated human communications that follow a set of organisation-specific rules E.g. rules of accounting, rules of report production, rules of addressing, etc. E.g. rules of accounting, rules of report production, rules of addressing, etc. 21 (Andras & Charlton, 2005) Communication networks in organisations How to capture the communication network nature of the organisation ?network Enron data 22 23 Organisational network dynamicsnetworks calculated for time periods (e.g. months) Network structure dynamics Organisation analysis Network structures clusters Network structures clusters How does the structure implied by the communication network match with the formally defined structure of the organisation ? How does the structure implied by the communication network match with the formally defined structure of the organisation ? Significant mismatches may indicate organisational problems Significant mismatches may indicate organisational problems How is the dynamics of the network is it diverging from or converging to the formal structure ? How is the dynamics of the network is it diverging from or converging to the formal structure ? 24 Communication rules Contents analysis of communications e.g. word stem frequencies, word consecutiveness networks, word patterns Contents analysis of communications e.g. word stem frequencies, word consecutiveness networks, word patterns Extraction of communication rules: pattern consecutiveness or pattern transition rules rule base of the organisation in average Extraction of communication rules: pattern consecutiveness or pattern transition rules rule base of the organisation in average 25 Decision making analysis Decisional processes represented as structured rule sets Decisional processes represented as structured rule sets Validation of the extracted decisional process by the management Validation of the extracted decisional process by the management Detection of deviations indicators of potential problems Detection of deviations indicators of potential problems 26 Document analysis Co-authorship networks / co- referencing networks Co-authorship networks / co- referencing networks Document clustering using word stem frequency vectors or word consecutiveness graphs Document clustering using word stem frequency vectors or word consecutiveness graphs 27 Work and group dynamics Dynamics of clusters of authors and papers structural dynamics and work topic dynamics Dynamics of clusters of authors and papers structural dynamics and work topic dynamics Detection of emerging work topics, merging groups, and drying up of work topics Detection of emerging work topics, merging groups, and drying up of work topics 28 Large-scale software systems E.g. Microsoft Windows + MS Office, Linux + Open Office, etc. E.g. Microsoft Windows + MS Office, Linux + Open Office, etc. Object oriented view: classes, messages, class instantiation object, software in action = objects sending messages and acting according to the received messages Object oriented view: classes, messages, class instantiation object, software in action = objects sending messages and acting according to the received messages 29 (Andras et al, 2006) Static analysis Network of classes linked by messages (calls) Network of classes linked by messages (calls) Search for vulnerability classes or messages that are the most critical for the integrity of the static network Search for vulnerability classes or messages that are the most critical for the integrity of the static network E.g. hubs, bottlenecks, cluster links E.g. hubs, bottlenecks, cluster links 30 Dynamic analysis The execution realisation of the software system may produce an object interaction graph that is differently weighted compared to the static class graph The execution realisation of the software system may produce an object interaction graph that is differently weighted compared to the static class graph Search for execution time vulnerabilities Search for execution time vulnerabilities 31 32 Summary 1 Many natural networks are scale-free networks Many natural networks are scale-free networks Such networks are robust to random damage, but sensitive to targeted damage Such networks are robust to random damage, but sensitive to targeted damage Brain area networks of macaque and cat are more similar to scale-free networks than to exponential networks Brain area networks of macaque and cat are more similar to scale-free networks than to exponential networks We looked for new antibiotic targets by analysing proteomes of bacteria. Network analysis reveals pairs/triplets of proteins that are potential drug targets. We looked for new antibiotic targets by analysing proteomes of bacteria. Network analysis reveals pairs/triplets of proteins that are potential drug targets. Summary 2 In ecological systems exposed to agricultural intervention food-web interaction network analysis can help to choose the least damaging intervention In ecological systems exposed to agricultural intervention food-web interaction network analysis can help to choose the least damaging intervention Social networks: determination of real structure and structural dynamics Social networks: determination of real structure and structural dynamics Software networks: static & dynamic analysis, real software reliability evaluation, experimental model for analysis of complex systems Software networks: static & dynamic analysis, real software reliability evaluation, experimental model for analysis of complex systems 33 34 Linking together Common feature: building blocks linked through interactions Common feature: building blocks linked through interactions Building blocks: neurons, proteins, species, humans, software components Building blocks: neurons, proteins, species, humans, software components Interactions: neuron spikes, temporary protein complex formation, food-web interactions, human communications, software communications Interactions: neuron spikes, temporary protein complex formation, food-web interactions, human communications, software communications Building blocks interacting units; interactions modify the state of interacting units on both sides of the interaction Building blocks interacting units; interactions modify the state of interacting units on both sides of the interaction 35 Complex systems Abstract view: interaction systems made of interactions between interacting units Abstract view: interaction systems made of interactions between interacting units (Charlton & Andras, 2007a; Andras & Charlton, 2005a; Andras & Charlton, 2005b; Andras & Andras, 2005) Roots: social systems theory of Niklas Luhmann, biological (autopoietic) systems theory of Francisco Varela and Humberto Maturana Roots: social systems theory of Niklas Luhmann, biological (autopoietic) systems theory of Francisco Varela and Humberto Maturana Complex systems Abstract interaction systems Complex systems Abstract interaction systems How do they maintain themselves by processing information about themselves and their environment ? How do they maintain themselves by processing information about themselves and their environment ? 36 Abstract interaction systems Theory of abstract interaction systems aim: to provide a common formal framework for theories of Luhmann, Varela & Maturana and generalize these Theory of abstract interaction systems aim: to provide a common formal framework for theories of Luhmann, Varela & Maturana and generalize these Current work combining inspiration from category theory interpretation of computation, dynamics of networks, pattern computation, computational learning, and other areas Current work combining inspiration from category theory interpretation of computation, dynamics of networks, pattern computation, computational learning, and other areas 37 Acknowledgements Network analysis: Network analysis: Marcus Kaiser, Olusola Idowu, Malcolm P Young, Panayiotis Periorelis, Agnes Madalinski, Steven Lynden, Robert Gwyther, Hermann Moisl, Abigail Haig, Greg Maniatopoulos, Will McElderry Marcus Kaiser, Olusola Idowu, Malcolm P Young, Panayiotis Periorelis, Agnes Madalinski, Steven Lynden, Robert Gwyther, Hermann Moisl, Abigail Haig, Greg Maniatopoulos, Will McElderry Complex systems theory Complex systems theory Bruce G Charlton Bruce G Charlton 38 Thank you!