GENERAL NETWORK PATTERNS All Complex Dynamic Networks Have Similar Structure in addition to Common Properties Hubs – The Celebrities of

GENERAL NETWORK PATTERNS All Complex Dynamic Networks Have Similar Structure in addition to Common Properties Hubs – The Celebrities of

GENERAL NETWORK PATTERNS All Complex Dynamic Networks Have Similar Structure in addition to Common Properties Hubs – The Celebrities of

Hawkins, Dave, News Director has reference to this Academic Journal, PHwiki organized this Journal GENERAL NETWORK PATTERNS Danail Bonchev Center as long as the Study of Biological Complexity Virginia Commonwealth University Singapore, July 9-17, 2007 All Complex Dynamic Networks Have Similar Structure in addition to Common Properties Scale-Freeness Small-Worldness Centrality Motifs Hubs Modules Hubs – The Celebrities of Network World Definition: Highly connected nodes Mits in addition to Reality of hubs connectivity Mark Vidal: “party” proteins in addition to “date” ones Mark Gerstein: Which of the multiple interactions occur simultaneously, in addition to which are mutually exclusive due to overlapping binding surfaces multi-interface ( “party”) in addition to single-interface (“date”) domains

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Mark Vidal’s “Party” in addition to “Date” Hubs J. D. Han et al. Nature 2004, 430, 88. The “party” hubs as long as m stable complexes; they are conserved The “date” hubs evolve across species Gerstein’s Single- in addition to Multiple Interface Hubs P. M. Kim, L. J. Lu, Y. Xia, M. B. Gerstein Science 2006, 314, 1938 Gerstein’s Single- in addition to Multiple Interface Hubs – 2

Gerstein’s Single- in addition to Multiple Interface Hubs – 3 Gerstein’s Single- in addition to Multiple Interface Hubs – 4 Some More About Hubs The good news in addition to the bad news Essentiality/Lethality Spreading of epidemics Side effects (medicines; gene engineering) The future of drug design in addition to patient treatment

Can Two Celebrities Work in a Team Assortativeness Protein interaction networks have negative assortitativeness Hubs connect with high correlation to low connectivity nodes Clustering Coefficient The larger the node clustering coefficient, the higher the local complexity E 3 3 4 5 6 Conn 0.5 0.5 0.667 0.833 1 Ci 0 0 0 1 ; 0.67 1 The average clustering coefficient of dynamic networks is much higher than that of r in addition to om networks Cprot (yeast) = 0.142 Cr in addition to = 0.00139 Can Supporting Actors Work Together Clustering vs. Local Connectivity in the Yeast Protein Interaction Network (AW Rives & T Galitski, PNAS, 100(2003)1128-1133)

Scale-Freeness What is scale-free Self-similarity, both globally in addition to locally. The presence of hubs irrespective of the scale of the network Topological invariance of a network structure, no matter how coarsely it is viewed. Barabasi, Albert, 1999: A network with a power-law degree distribution. (Price, 1965) Other mathematical laws: Dorogovtsev et al (2000), (exponential, polynomial, ) o Sole et al. (2002), Vazquez et al. (2003) – gene duplication generates power law distribution o Kuznetsov (2006): Not all networks are scale-free Preferential attachment The Power Law The Power Law In Intra-Cellular Networks (P. Fern in addition to ez, R.V. Solé, in Complexity in Chemistry, Biology, in addition to Ecology, D. Bonchev abd D.H. Rouvray, Eds. Springer, New York, 2005, p. 171)

Longevity Gene/Protein Network Power law Distribution (T. Witten, D. Bonchev, 2007) Small-Worldness Stanley Milgram, 1967 Six Degrees of Separation, Broadway, early 1990s Watts in addition to Strogatz, Nature, 1998 Small-Worldness vs Clustering Why is the network small-worldness important The normalized cluster coefficient in addition to the normalized network radius as a function of the probability of rewiring node-node links. The small-world effect is manifested with both small network radius in addition to high clustering coefficient.

The Concept of Node Centrality How to Define the Center of a Graph Classical definition: The graph center is the vertex(es) having the lowest eccentricity (F. Harary, Graph Theory, Addison-Wesley, 1969) Is this definition sufficient Centric vertex ordering: (1,2), (2,3,4,5,6,7) Hierarchical definition 2: If several vertices have the same eccentricity ei,the center is the vertex having the lowest vertex distance di. Other Hierarchical Criteria The network vertices are thus be characterized by their centrality, in addition to ordered in concentric circles around the central vertex(es). Graph Center – 2 Centric vertex ordering: (1,2), (2,3,4,5,6,7) {1},{2},{3},{4},{5,6},{7}

Network Centrality Closeness Centrality, (Freeman, 1978) Vertex Centrality, (Bonchev et al., 1980) Defined according to a set of hierarchically ordered criteria – eccentricity, vertex distance, DDS, Contradictions: 1: d1 = 4×1 + 1×2 + 1×3 = 9 CC(1) = 6/9 = 0.667 2: d2 = 2×1 + 4×2 = 10 > d1 CC(2) = 6/10 = 0.600 Node 1 is more central than node 2 However, e1 = 3 e2 = 2 < e1 Node 2 is more central than node 1 Betweenness Centrality (Freeman, 1978) Network Centrality - 2 The shortest paths are used only! Network Centrality - 3 Eigenvector Centrality (Bonacich, 1972) How to calculate the principal eigenvalue Eigenvector centralities are computed from the values of the first eigenvector of the graph adjacency matrix Why is centrality important Hawkins, Dave KZKE-FM News Director

All 13 types of connected subgraphs of three nodes Motifs – The Simple Building Blocks of Complex Networks Definition: Subgraphs occurring in complex networks at frequencies much higher than those in r in addition to omized networks (R. Milo et al., Science, 298, 2002, 824-827) Network Motifs – 2 Type of Motif Name Abundance in different kind of networks Network Motifs As Species Fingerprints

Network Motifs in addition to Dynamics Search as long as motifs with the fastest dynamics A. Apte, D. Bonchev, S. Fong (2007) Synthetic Biology FANMOD Software as long as Finding Network Motifs MFinder 1.2 Also there: Motif dictionary (by S. Wernicke in addition to F. Rasche) MAVisto (by F. Schreiber in addition to H. Schwobbermeyer)

Useful Software as long as Visualization in addition to Manipulation of Networks Pajek – default.htm Cytoscape – Pathway Studio 5.0 ( Ingenuity Patway Analysis – IPA 5.0 ( NetworkBlast – Do You See Any Internal Structure Here

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