Following are the list of standalone applications for network analysis:

Arena 3D

3D visualization of multi-layer networks

http://www.arena3d.org

Biana

Data integration and network management

http://sbi.imim.es/web/BIANA.php

BioLayout Express 3D 

2D/3D network visualization

http://www.biolayout.org/

BiologicalNetworks 

Efficient integrated multi-level analysis of microarray, sequence, regulatory and other data

http://www.biologicalnetworks.org

BioMiner

Modeling, analyzing and visualizing biochemical pathways and networks

http://www.zbi.uni-saarland.de/chair/projects/BioMiner

Cell Illustrator 

Petri nets for modeling and simulating biological networks

http://www.cellillustrator.com

COPASI

Analysis of biochemical networks and their dynamics

http://www.copasi.org/

Cytoscape 

Network visualization and analysis. Over 200 plugins [60]

http://www.cytoscape.org/

Dizzy

Chemical kinetics stochastic simulation software

http://magnet.systemsbiology.net/software/Dizzy/

DyCoNet

Gephi plugin that can be used to identify dynamic communities in networks

https://github.com/juliemkauffman/DyCoNet

GENeVis 

Network and pathway visualization

http://tinyurl.com/genevis/

GEPHI 

Interactive visualization and exploration for any network and complex system, dynamic and hierarchical graph.

https://gephi.org

Igraph

Collection of network analysis tools with the emphasis on efficiency, portability and ease of use

http://igraph.sourceforge.net

Medusa

Semantic and multi-edged simple networks

https://sites.google.com/site/medusa3visualization/

NAViGaTOR

Visualizing and analyzing protein-protein interaction networks

http://tinyurl.com/navigator1/

N-Browse

Interactive graphical browser for biological networks

http://www.gnetbrowse.org/

NeAT

Topological and clustering analysis of networks

http://rsat.ulb.ac.be/neat/

Ondex 

Data integration and visualization of large networks

http://www.ondex.org/

Osprey

Visualization and annotation of biological networks

http://biodata.mshri.on.ca/osprey/servlet/Index

Pajek 

Analysis and visualization of large networks and social network analysis

http://vlado.fmf.uni-lj.si/pub/networks/pajek/

PathwayAssist 

Navigation and analysis of biological pathways, gene regulation networks and protein interaction maps.

http://www.ariadnegenomics.com/downloads/

PIVOT 

Layout algorithms for visualizing protein interactions and families

http://acgt.cs.tau.ac.il/pivot/

ProCope 

Prediction and evaluation of protein complexes from purification data experiments

http://www.bio.ifi.lmu.de/Complexes/ProCope/

ProViz 

Visualization and exploration of interaction networks. Gene Ontology and PSI-MI formats supported

http://cbi.labri.fr/eng/proviz.htm

SpectralNET 

Network analysis and visualizations. Scatter plots and dimensionality reduction algorithms

https://www.broadinstitute.org/software/spectralnet

Tulip 

Enables the development of algorithms, visual encodings, interaction techniques, data models and domain-specific visualizations

http://tulip.labri.fr/TulipDrupal/

VANESA 

Automatic reconstruction and analysis of biological networks and Petri nets based on life-science database information

http://agbi.techfak.uni-bielefeld.de/vanesa/

VANTED 

Network reconstruction, data visualization, integration of various data types, network simulation

http://tinyurl.com/vanted/

yEd

Creation of diagrams manually and import external data

http://tinyurl.com/yEdGraph/

Web tools for network analysis

APID 

Unified protein-protein interactions from BIND, BioGRID, DIP, HPRD, IntAct and MINT

http://bioinfow.dep.usal.es/apid/

Arcadia 

Translates text-based descriptions of biological networks (SBML files) into standardized diagrams (Systems Biology Graphical Notation Process Description maps)

http://arcadiapathways.sourceforge.net/

AVIS 

Viewer for signaling networks

http://actin.pharm.mssm.edu/AVIS2

bioPIXIE 

Discovery of biological networks from diverse functional genomic data

http://pixie.princeton.edu/pixie

CellPublisher

Interactive representations of biochemical processes

http://cellpublisher.gobics.de/

Graphle

Distributed network exploration and visualization of interactive large, dense graphs

http://tinyurl.com/graphle/

GraphWeb 

Web server for graph-based analysis of biological networks

http://biit.cs.ut.ee/graphweb/

Hubba

Web-based service to explore the essential nodes in a network

http://hub.iis.sinica.edu.tw/Hubba

NetworkBLAST 

Analysis of protein interaction networks across species to infer protein complexes that are conserved in evolution

http://www.cs.tau.ac.il/~bnet/networkblast.htm

Pathview 

Tool set for pathway-based data integration and visualization

http://Pathview.r-forge.r-project.org/

PINA 

Integrated platform for protein interaction network construction, filtering, analysis, visualization and management

http://cbg.garvan.unsw.edu.au/pina/home.do

ReMatch 

Web-based tool for integration of user-given stoichiometric metabolic models into a database collected from public data sources

http://www.cs.helsinki.fi/group/sysfys/software/rematch/

SNOW 

Gene mapping on a reference or human protein-protein interaction network that SNOW hosts

http://snow.bioinfo.cipf.es

STITCH 

Resource to explore known and predicted interactions of chemicals and proteins

http://stitch.embl.de/

STRING

Protein interaction networks and integration of data such as genomic context, high-throughput experiments, conserved coexpression and previous knowledge derived from the literature

http://string-db.org

TVNViewer 

An interactive visualization tool for exploring networks that change over time or space

http://www.sailing.cs.cmu.edu/main/?page_id=545

tYNA 

System for managing, comparing and mining multiple networks

http://tyna.gersteinlab.org/tyna/

VisANT 

Visualization, mining, analysis and modeling of biological networks, metabolic networks and ecosystems

http://visant.bu.edu/