nametypegephiNetworkXgraphiacytoscape
Edge listtabularyesyesyesyes
Adjacency Listtabularyesyes
Adjacency Matrixtabularyesyes
GMLtextyesyesyesyes
GraphMLxmlyesyesyesyes
GEXFxmlyesyes
Pajek NETtabularyesyes
GraphViz DOTtextyesyes
GDFtabularyes
UCINET DLtextyes
Tulip TPLtextyes
Netdraw VNAtabularyes
LEDAyes
SparseGraph6textyes
MatrixMarkettextyes
Network Texttextyes
Cytoscape Exchangeyesyes
JSON Graphjsonyes
MATLAB data filesyes
Biopax OWLxmlyesyes
Cytoscape.js JSONjsonyesyes
Simple interaction fileyes
Nested network formatyes
XGMMLyes
SBMLyes

Not a full list. There is also all variations of RDF: N-Triples, N-Quads, Turtle, TriG and RDF/XML.