There is no other package around that satisfies all the following requirements: •Ability to handle large graphs efficiently •Embeddable into higher level environments (like R [6] or Python [7]) •Ability to be used for quick prototyping of new algorithms (impossible with “click & play” interfaces) •Platform-independent and open source igraph aims to satisfy all these requirements while possibly remaining easy to use in interactive mode as well.

The igraph software package for complex network research

(1) Klamer, A. D. “Some Results Concerning Polyominoes”. Fibonacci Q. 1965, 3(1), 9-20. (2) Golomb, S. W. Polyominoes·, Scribner, New York, 1965. (3) Harary, F.; Read, R. C. “The Enumeration of Tree-like Polyhexes”. Proc. Edinburgh Math. Soc. 1970, 17, 1-14. (4) Lunnon, W. F. “Counting Polyominoes” in Computers in Number Theory·, Academic: London, 1971; pp 347-372. (5) Lunnon, W. F. “Counting Hexagonal and Triangular Polyominoes”. Graph Theory Comput. 1972, 87-100. (6) Brunvoll, J.; Cyvin, S. J.; Cyvin, B. N. “Enumeration and Classification of Benzenoid Hydrocarbons”. J. Comput. Chem. 1987, 8, 189-197. (7) Balaban, A. T., et al. “Enumeration of Benzenoid and Coronoid Hydrocarbons”. Z. Naturforsch., A: Phys., Phys. Chem., Kosmophys. 1987, 42A, 863-870. (8) Gutman, I. “Topological Properties of Benzenoid Systems”. Bull. Soc. Chim., Beograd 1982, 47, 453-471. (9) Gutman, I.; Polansky, O. E. Mathematical Concepts in Organic Chemistry·, Springer: Berlin, 1986. (10) To3i6, R.; Doroslovacki, R.; Gutman, I. “Topological Properties of Benzenoid Systems—The Boundary Code”. MATCH 1986, No. 19, 219-228. (11) Doroslovacki, R.; ToSic, R. “A Characterization of Hexagonal Systems”. Rev. Res. Fac. Sci.-Univ. Novi Sad, Math. Ser. 1984,14(2) 201-209. (12) Knop, J. V.; Szymanski, K.; Trinajstic, N. “Computer Enumeration of Substituted Polyhexes”. Comput. Chem. 1984, 8(2), 107-115. (13) Stojmenovic, L; Tosió, R.; Doroslovaóki, R. “Generating and Counting Hexagonal Systems”. Proc. Yugosl. Semin. Graph Theory, 6th, Dubrovnik 1985; pp 189-198. (14) Doroslovaóki, R.; Stojmenovió, I.; Tosió, R. “Generating and Counting Triangular Systems”. BIT 1987, 27, 18-24. (15) Knop, J. V.; Miller, W. R.; Szymanski, K.; Trinajstic, N. Computer Generation of Certain Classes of Molecules·, Association of Chemists and Technologists of Croatia: Zagreb, 1985.

SMILES, a chemical language and information system. 1. introduction to methodology and encoding rules

1. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated structures 6. The tree-number 7. Determinant expansions 8. Vertex-partitions and the spectrum Part II. Colouring Problems: 9. The chromatic polynomial 10. Subgraph expansions 11. The multiplicative expansion 12. The induced subgraph expansion 13. The Tutte polynomial 14. Chromatic polynomials and spanning trees Part III. Symmetry and Regularity: 15. Automorphisms of graphs 16. Vertex-transitive graphs 17. Symmetric graphs 18. Symmetric graphs of degree three 19. The covering graph construction 20. Distance-transitive graphs 21. Feasibility of intersection arrays 22. Imprimitivity 23. Minimal regular graphs with given girth References Index.

Algebraic graph theory

This study focuses on the routing and WavelengthAssignment (RWA) problem in wavelength-routed optical WDM networks. Most of the attention is devoted to such networks operating under the wavelength-continuity constraint, in which lightpaths are set up for connection requests between node pairs, and a single lightpath must occupy the same wavelength on all of the links that it spans. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. If no wavelength is available for this lightpath on the selected route, then the connection request is blocked. We examine the RWA problem and review various routing approaches and wavelengthassignment approaches proposed in the literature. We also briefly consider the characteristics of wavelength-converted networks (which do not have the wavelength-continuity constraint), and we examine the associated research problems and challenges. Finally, we propose a new wavelengthassignment scheme, called Distributed Relative Capacity Loss (DRCL), which works well in distributed-controlled networks, and we demonstrate the performance of DRCL through simulation.

A Review of Routing and Wavelength Assignment Approaches for Wavelength- Routed Optical WDM Networks

Theories in “soft” areas of psychology lack the cumulative character of scientific knowledge. They tend neither to be refuted nor corroborated, but instead merely fade away as people lose interest. Even though intrinsic subject matter difficulties (20 listed) contribute to this, the excessive reliance on significance testing is partly responsible, being a poor way of doing science. Karl Popper’s approach, with modifications, would be prophylactic. Since the null hypothesis is quasi-always false, tables summarizing research in terms of patterns of “significant differences” are little more than complex, causally uninterpretable outcomes of statistical power functions. Multiple paths to estimating numerical point values (“consistency tests”) are better, even if approximate with rough tolerances; and lacking this, ranges, orderings, second-order differences, curve peaks and valleys, and function forms should be used. Such methods are usual in developed sciences that seldom report statistical significance. Consistency tests of a conjectural taxometric model yielded 94% success with zero false negatives.

Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology.

The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.

The graph isomorphism disease

An introduction to chromatic polynomials

Graph theory and computing

Backtrack algorithms for listing certain kinds of subgraphs of a graph are described and analyzed. Included are algorithms for listing all spanning trees, all cycles, all simple cycles, or all of c...

Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees

With over 10,000 diagrams and extensive tables of properties, this atlas is comprehensive and unique. Never before has so much visual information about graphs been collected in a single volume, making it an invaluable source for researchers in graph theory, operations research and computer science.

Ronald C. Read

Papers

The graph isomorphism disease

An introduction to chromatic polynomials

Graph theory and computing

Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees

An Atlas of Graphs