Pajek

Pajek (Slovenian for "spider") is a Windows program for the analysis and visualization of large networks, developed from 1996 onward by Vladimir Batagelj and Andrej Mrvar at the University of Ljubljana. Distributed free for non-commercial use, it became one of the standard tools in social network analysis, bibliometrics, and complex-systems research, and underpins the Cambridge University Press textbook "Exploratory Social Network Analysis with Pajek." Its defining characteristic is scale: through efficient sparse data structures it handles networks with millions of vertices on ordinary hardware, and the sibling builds Pajek-XXL and Pajek-3XL push the ceiling to roughly two and ten billion vertices respectively by trading memory footprint against speed, sizes that GUI tools such as Gephi, Cytoscape, and Tulip cannot reach.

Pajek's model is built around several distinct object types rather than a single graph. A network holds vertices and directed arcs and/or undirected edges (optionally multi-relational, temporal, or two-mode); a partition assigns each vertex an integer class; a vector assigns each vertex a real value; a permutation reorders vertices; and hierarchies and clusters organize subsets. Analytical operations transform between these objects, for example computing degree, betweenness or closeness centrality into a vector, deriving components or k-cores into a partition, or extracting and shrinking subnetworks. Pajek is also known for generalized blockmodeling, cohesion and cluster analysis, acyclic-network and citation-flow analysis, shortest paths, and layout algorithms including Kamada-Kawai and Fruchterman-Reingold energy layouts.

The native serialization is the plain-text Pajek NET (.net) format, documented as Pajek in this catalog. A *Vertices n header is followed by numbered vertex lines carrying an optional quoted label, x/y/z coordinates, and visual attributes such as ic (interior color) and s_size; connections appear under *Arcs (directed) and *Edges (undirected), or compactly under *Arcslist/*Edgeslist, with an optional third column giving the line value/weight. A *Matrix section can store the adjacency matrix directly. Companion files .clu, .vec, and .per hold partitions, vectors, and permutations. Pajek imports and exports common interchange formats including GML, GraphML, UCINET DL (UCINET), and DOT, and can output SVG and VRML for presentation, making it a frequent hub in format-conversion pipelines alongside libraries like igraph and NetworkX, which both read and write NET files.

Its main limitations are practical rather than analytical: it is closed-source and Windows-only (run via emulation elsewhere), the classic edition uses 32-bit vertex indexing, the modal-dialog GUI has a steep learning curve, and scripting is confined to macros rather than a general programming API, so reproducible workflows often pair it with external scripting tools.